Use the Product Rule of Exponents to simplify 5^10⋅5^5(1 point)
5^15
5^50
25^15
25^50
5^10⋅5^5 can be simplified using the Product Rule of Exponents as 5^(10+5) which equals 5^15.
So the answer is 5^15.
Find the numerical equivalent of 9^9⋅9^−6.(1 point)
To find the numerical equivalent of 9^9⋅9^(-6), we can use the Product Rule of Exponents, which states that when you multiply two numbers with the same base, you add their exponents.
9^9⋅9^(-6) can be rewritten as 9^(9 + (-6)).
9^9 is simply 9 multiplied by itself 9 times, so it equals 387,420,489.
9^(-6) means taking the reciprocal of 9^6. Since 9^6 is 531,441, the reciprocal is 1/531,441.
So, 9^(-6) is equal to 1/531,441.
Now we can find the numerical equivalent of 9^9⋅9^(-6) by multiplying the two values together:
(9^9)⋅(9^(-6)) = 387,420,489 * (1/531,441)
Simplifying the fraction gives us:
(9^9)⋅(9^(-6)) = 387,420,489/531,441
So, the numerical equivalent of 9^9⋅9^(-6) is approximately 0.729.
What is the missing exponent in the following equation?
h^450/h? = h^215
To find the missing exponent, we can use the Quotient Rule of Exponents, which states that when you divide two numbers with the same base, you subtract their exponents.
In this case, we know that h^450 divided by h is equal to h^215. To find the missing exponent, we subtract the exponent of h in the denominator from the exponent of h in the numerator.
So, the missing exponent is:
450 - 1 = 449
Therefore, the missing exponent is 449.
Simplify 12^87÷12^25
To simplify 12^87 ÷ 12^25, we can use the Quotient Rule of Exponents, which states that when you divide two numbers with the same base, you subtract the exponents.
Using this rule, we subtract the exponent of 12 in the denominator from the exponent of 12 in the numerator:
12^87 ÷ 12^25 = 12^(87-25)
Simplifying the exponent gives us:
12^62
Therefore, the simplified expression is 12^62.
What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12?
To find the missing number in the simplified exponential expression, we can use the Quotient Rule of Exponents. According to the Quotient Rule, when dividing two numbers with the same base, we subtract the exponent in the denominator from the exponent in the numerator.
In this case, the expression "7^? ÷ 7^5 = 7^12 ?" implies that the exponent in the numerator is equal to the exponent in the denominator plus 12.
So, the missing number is:
? = 5 + 12 = 17
Therefore, the missing number in the simplified exponential expression is 17.
What is the value of 6.9−2^0?
4.9
5.9
6.9
7.9
The value of 6.9-2^0 can be found by simplifying the expression step by step.
First, we evaluate 2^0, which is equal to 1. Therefore, the expression becomes:
6.9 - 1
Next, we perform the subtraction:
6.9 - 1 = 5.9
Therefore, the value of 6.9-2^0 is 5.9.
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0)
9⋅(−33)^0+3/2(8−27^0) =
⋅
+3/2(
–
)
Applying the Zero Power Rule states that any non-zero number raised to the power of 0 is equal to 1.
So, in the expression 9⋅(−33)^0, we know that (-33)^0 equals 1.
Therefore, we can simplify the expression to:
9⋅1 + 3/2(8 - 1)
Simplifying further:
9 + 3/2(7)
Multiplying 3/2 by 7:
9 + 21/2
To add the fractions, we need a common denominator:
9 + (21/2) * (2/2) = 9 + 42/2
Combining the fractions:
9 + 42/2 = 9 + 21
Final answer:
9 + 21 = 30
Solve the expression 15⋅8^0/5 + 4(7^0−6).
15⋅8^0/5+4(7^0−6)=
To solve the expression, we'll start by evaluating the exponent expressions.
Starting with 8^0, any number (except 0) raised to the power of 0 is always equal to 1. So, 8^0 = 1.
Next, 7^0 is also equal to 1.
Now we can rewrite the expression:
15⋅8^0/5 + 4(7^0−6)
Since 8^0 = 1 and 7^0 = 1, the expression becomes:
15⋅1/5 + 4(1−6)
Next, we simplify inside the parentheses:
15/5 + 4(1−6)
15/5 equals 3, and 1−6 equals -5, so the expression is now:
3 + 4(-5)
Multiplying 4 by -5:
3 + (-20)
Combining the terms:
3 - 20 = -17
Therefore, the solution to the expression is -17.
Use the Power Rule of Exponents to simplify (10^3)^6
The Power Rule of Exponents states that when an exponent is raised to another exponent, we multiply the exponents.
In this case, we have (10^3)^6. To simplify, we multiply the exponents:
(10^3)^6 = 10^(3*6) = 10^18
So, the simplified expression is 10^18.
f the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
(7^18)^3
(7⋅7⋅7⋅7⋅7)^10
(7^10)^5
The expanded equivalent expression of 7^15, using the Power Rule of Exponents, would be:
(7⋅7⋅7⋅7⋅7)^10
So, the correct option is (7⋅7⋅7⋅7⋅7)^10.
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9
To simplify the expression (19^4)^9 using the Power Rule of Exponents, we multiply the exponents.
(19^4)^9 is equal to 19^(4 * 9).
Simplifying the exponent:
19^(4 * 9) = 19^36
So, the simplified equivalent expression for (19^4)^9 is 19^36.
Apply the Property of Negative Integer Exponents to solve 7^−3. The answer should not contain any exponent expression or decimals.
7^−3=
Applying the Property of Negative Integer Exponents, we can rewrite 7^(-3) as the reciprocal of 7^3.
Therefore, 7^(-3) is equal to 1/(7^3).
Simplifying 7^3, we have:
7^(-3) = 1/(7 * 7 * 7)
Simplifying the multiplication:
7^(-3) = 1/343
So, the solution to 7^(-3) is 1/343.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only.
3^−17/8^−14=
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 3^(-17)/8^(-14) with positive exponents only, we can reciprocate both terms.
Reciprocating 3^(-17), we get 1/3^17.
Reciprocating 8^(-14), we get 1/8^14.
Therefore, the expression 3^(-17)/8^(-14) is equivalent to (1/3^17)/(1/8^14).
To simplify this further, we divide the numerators and denominators:
(1/3^17)/(1/8^14) = (8^14)/(3^17).
So, the expression equivalent to 3^(-17)/8^(-14) with positive exponents only is (8^14)/(3^17).