Use the product rule of exponents simplify 3^5 * 3^7
To simplify the expression, we can apply the product rule of exponents, which states that when multiplying two exponential expressions with the same base, you can add their exponents.
3^5 * 3^7 = 3^(5+7) = 3^12
Therefore, 3^5 * 3^7 simplifies to 3^12.
find the numerical equivalent of 5^10 * 5^-6
To find the numerical equivalent of 5^10 * 5^-6, we can simplify the expression using the product rule of exponents and then compute the result.
Using the product rule, we add the exponents of the same base:
5^10 * 5^-6 = 5^(10 + (-6)) = 5^4
Therefore, 5^10 * 5^-6 is equal to 5^4.
Now, let's evaluate 5^4:
5^4 = 5 * 5 * 5 * 5 = 625
So, the numerical equivalent of 5^10 * 5^-6 is 625.
What is the missing exponent in the following equation?
8^500 / 8^? = s^175
To find the missing exponent in the equation 8^500 / 8^? = s^175, we can apply the quotient rule of exponents.
The quotient rule states that when dividing exponential expressions with the same base, you subtract their exponents.
So, in this case, we have:
8^500 / 8^? = s^175
Using the quotient rule, we can subtract the exponent of 8 on the right side of the equation from the exponent on the left side:
8^500 / 8^? = s^175
8^(500 - ?) = s^175
To find the missing exponent, we need to match the exponents on the left and right sides of the equation. Since 8^500 is not equal to s^175, there is no specific value for the missing exponent that will make the equation true.
What is the missing exponent in the following equation? s^500/s^?=s^175
To find the missing exponent in the equation s^500 / s^? = s^175, we can apply the quotient rule of exponents.
The quotient rule states that when dividing exponential expressions with the same base, you subtract their exponents.
So, in this case, we have:
s^500 / s^? = s^175
Using the quotient rule, we can subtract the exponent of s on the right side of the equation from the exponent on the left side:
s^(500 - ?) = s^175
To find the missing exponent, we need to match the exponents on the left and right sides of the equation.
Since the bases are the same (s), in order for the equation to be true, the exponents must also be equal:
500 - ? = 175
To find the missing exponent (?), we can subtract 175 from 500:
500 - ? = 175
? = 500 - 175
? = 325
Therefore, the missing exponent in the equation s^500 / s^? = s^175 is 325.
What is the missing number in this simplified exponential expression:
8^? / 8^4 = 8^15?
To find the missing number in the equation 8^? / 8^4 = 8^15?, we can apply the quotient rule of exponents.
The quotient rule states that when dividing exponential expressions with the same base, you subtract their exponents.
So, in this case, we have:
8^? / 8^4 = 8^15?
Using the quotient rule, we can subtract the exponent of 8 on the right side of the equation from the exponent on the left side:
8^(? - 4) = 8^15?
To find the missing number, we need to match the exponents on the left and right sides of the equation.
Since the base is the same (8), in order for the equation to be true, the exponents must also be equal:
? - 4 = 15?
To solve for the missing number (?), we can subtract 15? from both sides:
? - 15? = 4
Combining like terms:
-14? = 4
Dividing both sides by -14:
? = 4 / -14
Simplifying:
? = -2/7
Therefore, the missing number in the equation 8^? / 8^4 = 8^15? is -2/7.
What is the missing number in this simplified exponential expression:
8^? / 8^4 = 8^15
To find the missing number in the equation 8^? / 8^4 = 8^15, we need to compare the exponents on each side of the equation.
We have:
8^? / 8^4 = 8^15
To combine the two sides of the equation with the same base (8), we can subtract the exponent of 8 on the right side from the exponent on the left side:
8^(? - 4) = 8^15
To find the missing number (?), the exponents on both sides must be equal. Therefore, we can set the exponent of 8 on the left side equal to the exponent of 8 on the right side:
? - 4 = 15
Solving for ?, we can add 4 to both sides of the equation:
? = 15 + 4
? = 19
Therefore, the missing number in the equation 8^? / 8^4 = 8^15 is 19.
Apply the Zero Power Rule to create an equivalent expression to
(-40)^0 + 1/2(11 - 32^0)
The Zero Power Rule states that any non-zero number raised to the power of zero is equal to 1.
Applying the Zero Power Rule to the expression (-40)^0, we get:
(-40)^0 + 1/2(11 - 32^0) = 1 + 1/2(11 - 1)
Since any number multiplied by 1 is that number itself, we can simplify further:
= 1 + 1/2(10)
= 1 + 5
= 6
Therefore, the equivalent expression to (-40)^0 + 1/2(11 - 32^0) is 6.
Which of the following expressions can be simplified to give an answer of 1?
15−(9.1)015−(9.1)015 minus 9 point 1 to the 0 power(−5.22)0(−5.22)0negative 5 point 2 2 to the 0 power110+240110+24011 to the 0 power plus 24 to the 0 power2(80)
Expressions that can be simplified to give an answer of 1 are those where any number raised to the power of 0 will yield 1. Let's evaluate each expression:
1. 15−(9.1)0 = 15−1 = 14
2. (−5.22)0 = 1
3. 110+240 = 1 + 0 = 1
4. 11 to the 0 power plus 24 to the 0 power = 1 + 1 = 2
5. 2(80) cannot be simplified to give an answer of 1.
From the given expressions, the only one that can be simplified to give an answer of 1 is (−5.22)0.
Which of the following expressions can be simplified to give an answer of 1?
15 - (9.1)^0
(-5.22)^0
11^0 + 24^0
2 (8^0)
To identify which expressions can be simplified to give an answer of 1, we need to look for any terms with exponents of 0.
Let's evaluate each expression:
1. 15 - (9.1)^0 = 15 - 1 = 14. This expression does not simplify to 1.
2. (-5.22)^0 = 1. Any nonzero number raised to the power of 0 is equal to 1.
3. 11^0 + 24^0 = 1 + 1 = 2. This expression does not simplify to 1.
4. 2(8^0) = 2 * 1 = 2. This expression does not simplify to 1.
Therefore, the only expression that can be simplified to give an answer of 1 is (-5.22)^0.
Use the power rule of exponents to simplify the expression
(x^6)^5
To simplify the expression (x^6)^5 using the power rule of exponents, we multiply the exponents.
According to the power rule, (a^m)^n = a^(m*n).
Therefore, (x^6)^5 is equal to x^(6*5).
Simplifying the exponent: 6 * 5 = 30.
Therefore, (x^6)^5 simplifies to x^30.
which of the following is equivalent to 3^-4?
81
-81
1/3^-4
1/81
To simplify 3^(-4), we use the rule that states any term raised to the power of -n is equivalent to 1 divided by that term raised to the power of n.
Therefore, 3^(-4) is equivalent to 1/3^4, which is equal to 1/81.
So, the expression equivalent to 3^(-4) is 1/81.
Apply the property of negative integer exponents to find the numerical equivalent of 8^-3. The answer should not contain any exponent expression or decimal.
The property of negative integer exponents states that any number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent.
In this case, 8^(-3) is equivalent to 1/8^3.
Now, let's evaluate 8^3:
8^3 = 8 * 8 * 8 = 512
Therefore, 8^(-3) is equal to 1/512.
Complete the table. For each of the expressions, choose which exponent rule has been used to simplify.(3 points)Product Rule Quotient Rule Power Rule Negative Integer Exponent Rule Zero Power Rule(163)9= 1627(163)9= 1627Product Rule – (163)9= 1627(163)9= 1627Quotient Rule – (163)9= 1627(163)9= 1627Power Rule – (163)9= 1627(163)9= 1627Negative Integer Exponent Rule – (163)9= 1627(163)9= 1627Zero Power Rule – (163)9= 1627(163)9= 16276−129−15=9156126−129−15=915612Product Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th powerQuotient Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th powerPower Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th powerNegative Integer Exponent Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th powerZero Power Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th power11801122=115811801122=1158Product Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th powerQuotient Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th powerPower Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th powerNegative Integer Exponent Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th powerZero Power Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th power
Here is the completed table:
Expression Exponent Rule Used
(163)^9 = 16^27 Power Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Quotient Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Negative Integer Exponent Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Product Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Zero Power Rule
11^80 / 11^22 = 11^58 Quotient Rule
11^80 / 11^22 = 11^58 Negative Integer Exponent Rule
11^80 / 11^22 = 11^58 Power Rule
11^80 / 11^22 = 11^58 Product Rule
11^80 / 11^22 = 11^58 Zero Power Rule
Complete the table. For each of the expressions, choose which exponent rule has been used to simplify.(3 points)
Product Rule Quotient Rule Power Rule Negative Integer Exponent Rule Zero Power Rule (163)9= 1627(163)9= 1627 – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th power Quotient Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th power Power Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th power Negative Integer Exponent Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th power Zero Power Rule – the fraction with numerator 6 to the negative 12 power and denominator 9 to the negative 15 power is equal to the fraction with numerator 9 to the 15th power and denominator 6 to the 12th power11801122=115811801122=1158Product Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th power Quotient Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th power Power Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th power Negative Integer Exponent Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th power Zero Power Rule – the fraction with numerator 11 to the 80th power and denominator 11 to the 22th power is equal to 11 to the 58th power
Here is the completed table:
Expression Exponent Rule Used
(163)^9 = 16^27 Power Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Quotient Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Negative Integer Exponent Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Product Rule
6^(-12) / 9^(-15) = 9^15 / 6^12 Zero Power Rule
11^80 / 11^22 = 11^58 Quotient Rule
11^80 / 11^22 = 11^58 Power Rule
11^80 / 11^22 = 11^58 Negative Integer Exponent Rule
11^80 / 11^22 = 11^58 Product Rule
11^80 / 11^22 = 11^58 Zero Power Rule
Apply the properties of integer Exponents to generate an equivalent expression to (5^-3)^6 * 5^17 / 10^-2 with only positive exponents, then solve the expression.
To generate an equivalent expression with only positive exponents, we can use the properties of integer exponents and simplify the expression:
(5^-3)^6 * 5^17 / 10^-2
First, we can apply the power of a power property by multiplying the exponents:
(5^(-3 * 6)) * 5^17 / 10^-2
Simplifying the exponent:
(5^-18) * 5^17 / 10^-2
Next, we can apply the quotient rule of exponents by subtracting the exponents:
5^(-18 - 17) / 10^-2
Simplifying the exponents:
5^-35
Select all terms that are equivalent to 4^3 / 4^5
-4^2
4^2
4^-2
1/4^2
1/16