Question

apply the properties of integer exponents to generate an equivalent expression to
(5^ -3)^6*5^17/10^-2

Answer 1

To generate an equivalent expression, we can apply the properties of integer exponents.

First, we simplify the expression inside the parentheses: (5^ -3)^6.
Using the property (a^m)^n = a^(m*n), we can rewrite this as 5^(-3*6) = 5^(-18).

Next, we simplify the expression 5^17.

Using the property a^m/a^n = a^(m-n), we can rewrite 5^17/10^-2 as 5^(17-(-2)) = 5^(17+2) = 5^19.

Now, we have (5^ -3)^6 * 5^17/10^-2 = 5^-18 * 5^19.

Using the property a^m * a^n = a^(m+n), we can simplify this to 5^(-18+19) = 5^1.

Therefore, an equivalent expression is 5.