Exponent Rules Unit Test
Use the product rule of exponents to simplify 5^10 * 5^5
responses
a. 5^15
b. 25^15
c. 25^50
d. 5^50
To find the numerical equivalent of 9^3, we need to evaluate the expression.
9^3 means multiplying 9 by itself three times.
9^3 = 9 * 9 * 9 = 729
So, the numerical equivalent of 9^3 is 729.
2^0 is equal to 1, so the expression 6.9 - 2^0 becomes 6.9 - 1.
6.9 - 1 = 5.9.
Therefore, the value of 6.9 - 2^0 is 5.9.
So the correct answer is: d. 5.9
To create an equivalent expression for the problem:
9 * (-33)^0 + 3/2 * (8 - 27^0)
Using the zero power rule, we know that any non-zero number raised to the power of 0 equals 1. Therefore, (-33)^0 is equal to 1.
So, the expression becomes:
9 * 1 + 3/2 * (8 - 1)
Simplifying further:
9 + 3/2 * 7
To multiply a fraction by a whole number, we can multiply the numerator by the whole number:
9 + (3 * 7) / 2
9 + 21/2
To add fractions with a common denominator, we add the numerators:
(18/2 + 21/2) / 2
39/2 / 2
To divide a fraction by a whole number, we multiply the numerator by the reciprocal of the whole number:
39/2 * 1/2
39/4
So, an equivalent expression for the problem is:
9 * (-33)^0 + 3/2 * (8 - 27^0) = 39/4
The product rule of integer exponents states that when multiplying two numbers with the same base, you add their exponents.
To find the numerical equivalent of 12^-5 * 12^7, we can apply the product rule and add the exponents:
12^-5 * 12^7 = 12^(-5 + 7)
Simplifying the exponent, -5 + 7 = 2.
Therefore, 12^-5 * 12^7 simplifies to 12^2.
To find the numerical value, we can calculate 12^2:
12^2 = 144.
So, the numerical equivalent of 12^-5 * 12^7 is 144.
The product rule of exponents states that when multiplying two numbers with the same base, you add their exponents.
Therefore, 5^10 * 5^5 would simplify to 5^(10+5), which is equivalent to 5^15.
So the correct answer is: a. 5^15
Find the numerical equivalent of 9^9 * 9^-6
When multiplying two numbers with the same base but different exponents, you subtract the exponent of the second number from the exponent of the first number.
Therefore, 9^9 * 9^-6 would simplify to 9^(9 - 6), which is equivalent to 9^3.
So the numerical equivalent of 9^9 * 9^-6 is 9^3.
Find the numerical equivalent of 9^3
what is the missing exponent in the following equation?
h^420/h^? = h^215
To find the missing exponent in the equation h^420/h^? = h^215, we can use the quotient rule of exponents.
According to the quotient rule of exponents, when dividing two numbers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
Therefore, h^420/h^? is equal to h^(420 - ?).
The equation h^420/h^? = h^215 can be written as h^(420 - ?) = h^215.
To match the exponents on both sides of the equation, we set the exponents equal to each other:
420 - ? = 215
Now, we solve for ?:
420 - 215 = ?
205 = ?
Therefore, the missing exponent in the equation is 205.
Simplify 12^87 divide 12^25
To simplify 12^87 / 12^25, we can use the quotient rule of exponents, which states that when dividing two numbers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
Therefore, 12^87 / 12^25 can be simplified to 12^(87-25).
Simplifying the exponent, 87 - 25 = 62.
So, 12^87 / 12^25 simplifies to 12^62.
What is the missing number in this simplified exponential expression:
7^? divide 7^5 = 7^12
To find the missing number in the simplified expression 7^? / 7^5 = 7^12, we can use the quotient rule of exponents.
According to the quotient rule of exponents, when dividing two numbers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
In this case, we have:
7^? / 7^5 = 7^12
Using the quotient rule, we can simplify this to:
7^(? - 5) = 7^12
In order for this equation to hold true, the exponent on both sides must be equal.
Therefore, we have:
? - 5 = 12
To find the missing number, we solve this equation for ?:
? = 12 + 5
? = 17
So, the missing number in the simplified expression is 17.
What is the value of 6.9 - 2^0
responses
a. 7.9
b. 6.9
c. 4.9
d. 5.9
Apply the zero power rule to create an equivalent expression to
9* (-33)^0 + 3/2*(8 - 27^0)
Use this as a base
? * ? + 3/2 (? - ?)
The zero power rule states that any non-zero number raised to the power of 0 equals 1.
Using the zero power rule, we can simplify the expression:
9 * (-33)^0 + 3/2 * (8 - 27^0)
Since (-33)^0 is equal to 1, the expression becomes:
9 * 1 + 3/2 * (8 - 1)
= 9 + 3/2 * 7
= 9 + 21/2
To simplify further, we need a common denominator for the addition of fractions:
9 + (21/2) * (2/2)
This becomes:
9 + 42/2
= 9 + 21
= 30
So, the equivalent expression using the base provided is:
? * ? + 3/2 (? - ?) = 30
create an equivalent expression for that problem
solve the expression 15*8^0/5 + 4 (7^0 - 6)
Let's solve the expression step-by-step:
15 * 8^0 / 5 + 4 * (7^0 - 6)
First, we simplify 8^0 using the zero power rule:
8^0 is equal to 1.
So the expression becomes:
15 * 1 / 5 + 4 * (7^0 - 6)
Now, we simplify 7^0 using the zero power rule:
7^0 is equal to 1.
The expression further simplifies to:
15 * 1 / 5 + 4 * (1 - 6)
Now we simplify the expression within the parentheses:
15 * 1 / 5 + 4 * (-5)
Next, we perform multiplication:
15/5 + 4 * (-5)
Now we simplify the division:
3 + 4 * (-5)
Finally, we perform the remaining multiplication and addition:
3 + (-20)
The final answer is:
-17
Use the power rule of exponents to simplify (10^3)^6
The power rule of exponents states that when you raise a power to another power, you multiply the exponents.
Therefore, to simplify (10^3)^6, we multiply the exponents:
(10^3)^6 = 10^(3*6)
= 10^18
So, (10^3)^6 simplifies to 10^18.
Use the power rule of exponents to create a simplified equivalent expression for (19^4)^9
The power rule of exponents states that when you raise a power to another power, you multiply the exponents.
Therefore, to create a simplified equivalent expression for (19^4)^9, we multiply the exponents:
(19^4)^9 = 19^(4*9)
= 19^36
So, a 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.
The property of negative integer exponents states that when you have a negative exponent, you can rewrite the expression by taking the reciprocal of the base and changing the sign of the exponent to positive.
Therefore, to solve 7^-3 using the property of negative exponents:
7^-3 = 1 / 7^3
Taking the reciprocal of 7 and changing the exponent to positive 3 gives:
1 / (7 * 7 * 7)
Simplifying further:
1 / 343
So, the solution to 7^-3 without any exponent expressions or decimals is 1/343.
Apply the property of negative integer exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only
To apply the property of negative integer exponents and generate an expression equivalent to 3^-17/8^-14 with positive exponents only, we can rewrite the expression using the reciprocal of the base and changing the sign of the exponent accordingly.
3^-17 / 8^-14
Applying the property of negative exponents:
= 1 / (3^17 * 1/8^14)
Next, simplifying further:
= 1 / (1 / 3^17 * 8^14)
To convert the reciprocal back to a positive exponent, we can invert the fraction:
= (3^17 * 8^14) / 1
This expression is now equivalent to 3^-17 / 8^-14 but with positive exponents only.
apply the properties of integer exponents to generate equivalent expressions to (7^-3)^7 * 7^20/6^-2 with positive exponents, then solve the expression. provide the answer as an improper fraction.
To generate equivalent expressions to (7^-3)^7 * 7^20 / 6^-2 with positive exponents, we can apply the property of integer exponents.
First, let's simplify (7^-3)^7:
(7^-3)^7 is equivalent to 7^(-3 * 7), which simplifies to 7^-21.
Next, let's simplify 7^20 / 6^-2:
7^20 / 6^-2 is equivalent to 7^20 * 6^2, since dividing by a negative exponent is the same as multiplying by the positive exponent of the reciprocal.
Therefore, the expression becomes 7^-21 * 7^20 * 6^2.
To solve the expression, we can combine the bases with the same exponent:
7^-21 * 7^20 * 6^2
Since 7^(-21) * 7^20 is equivalent to 7^(-1) (given that (-21) + 20 is equal to -1):
7^-1 * 6^2
Notice that 7^-1 is the reciprocal of 7^1, also known as 1/7^1, so:
1/7 * 6^2
Finally, we can calculate 6^2, which is equal to 36:
1/7 * 36
This simplifies to:
36/7
Therefore, the answer as an improper fraction is 36/7.