Question
Apply the Properties of Integer Exponents to generate an equivalent expression to (5^−3)6⋅ 5^17/10^−2 (1 point)
a. 1/20
b. 20
c. 1/500
d. 500
a. 1/20
b. 20
c. 1/500
d. 500
Answers
Answered by
GPT 3.5
To generate an equivalent expression, we can use the property of integer exponents that states a^m ÷ a^n = a^(m-n).
So, we can rewrite the expression as:
(5^(-3+17))/(10^-2)
Simplifying the exponents, we get:
= 5^14 / 10^-2
Now, using the property of integer exponents again, we can rewrite this as:
= 5^14 × 10^2
Finally, simplifying the expression, we have:
= (5^2)^(14/2) × 10^2
= 25^7 × 10^2
= 50^7
Therefore, the equivalent expression is 50^7.
The answer is not provided in the options given.
So, we can rewrite the expression as:
(5^(-3+17))/(10^-2)
Simplifying the exponents, we get:
= 5^14 / 10^-2
Now, using the property of integer exponents again, we can rewrite this as:
= 5^14 × 10^2
Finally, simplifying the expression, we have:
= (5^2)^(14/2) × 10^2
= 25^7 × 10^2
= 50^7
Therefore, the equivalent expression is 50^7.
The answer is not provided in the options given.
Answered by
GPT 3.5
Apologies for missing that step.
We have:
(5^(-3))6 × 5^17 / 10^(-2)
First, let's simplify the negative exponents:
1/(5^3) × 6 × 5^17 / (1/(10^2))
Now, let's simplify the fractions:
6 × (5^17) × (10^2) / (5^3)
Using the property of integer exponents, we can rewrite (5^17) as (5^3) × (5^14):
6 × (5^3) × (5^14) × (10^2) / (5^3)
Now, cancel out the common factors:
6 × (5^14) × (10^2)
Since (10^2) equals 100, we can rewrite the expression as:
6 × (5^14) × 100
Finally, we can combine the constants:
600 × (5^14)
Therefore, the equivalent expression is 600 × (5^14).
The answer is not provided in the options given.
We have:
(5^(-3))6 × 5^17 / 10^(-2)
First, let's simplify the negative exponents:
1/(5^3) × 6 × 5^17 / (1/(10^2))
Now, let's simplify the fractions:
6 × (5^17) × (10^2) / (5^3)
Using the property of integer exponents, we can rewrite (5^17) as (5^3) × (5^14):
6 × (5^3) × (5^14) × (10^2) / (5^3)
Now, cancel out the common factors:
6 × (5^14) × (10^2)
Since (10^2) equals 100, we can rewrite the expression as:
6 × (5^14) × 100
Finally, we can combine the constants:
600 × (5^14)
Therefore, the equivalent expression is 600 × (5^14).
The answer is not provided in the options given.
Answered by
GPT 3.5
I apologize for any confusion caused by the incorrect exponent. Given that the exponent 5^17 is not feasible, it seems there may indeed be a typo or mistake in the problem statement. Without the correct information, it is not possible to generate an equivalent expression.
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