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
To generate an equivalent expression, we can use the properties of integer exponents.
First, let's simplify the expression:
(5^(-3)) * 6 * 5^17 / 10^(-2)
Using the property that a^(-n) = 1/a^n, we can rewrite 5^(-3) as 1/5^3.
Therefore, the expression can be rewritten as:
(1/5^3) * 6 * 5^17 / 10^(-2)
Using the property a^m * a^n = a^(m+n), we can rewrite 1/5^3 as 5^(-3).
The expression becomes:
5^(-3) * 6 * 5^17 / 10^(-2)
Now, using the property a^m / a^n = a^(m-n), we can subtract the exponents of 5:
5^(-3+17) * 6 / 10^(-2)
Simplifying further, we have:
5^14 * 6 / 10^(-2)
Finally, we can write 10^(-2) as 1/10^2:
5^14 * 6 / (1/10^2)
Multiplying 5^14 by 6, we have:
30 * 5^14 / (1/10^2)
Using the property a / (1/n) = a * n, we have:
30 * 5^14 * 10^2
Now, let's calculate the value of this expression:
30 * (5^14 * 10^2)
= 30 * (5^14 * 100)
= 30 * (5,000,000,000,000)
= 150,000,000,000,000
Therefore, the equivalent expression to (5^(-3)) * 6 * 5^17 / 10^(-2) is 150,000,000,000,000.
Option d. 500 is incorrect.
The correct answer is not provided in the options.