Question

Which of the following is the equivalent expression to (15^−3x 4^7)^0/4^-3 that has been generated by applying the Properties of Integer Exponents?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equivalent expression using properties of integer exponents, we follow these rules:

1. When raising a power to another power, we multiply the exponents: (a^m)^n = a^(m*n)
2. When dividing two powers with the same base, we subtract the exponents: a^m / a^n = a^(m-n)
3. When raising a product to a power, we raise each factor to that power: (a*b)^n = a^n * b^n

First, let's simplify the expression within the parentheses:
15^(-3x) * 4^7 = (3*5)^(-3x) * 2^(7*2) = 3^(-9x) * 2^14

Now, let's combine the exponents using rule 3:
(15^(-3x) * 4^7)^0 / 4^(-3) = (3^(-9x) * 2^14)^0 / 2^(-6) =
(3^(-9x))^0 * (2^14)^0 / 2^(-6) =
1 * 1 / 2^(-6) = 1 / (1 / 2^6) = 1 * 2^6 =
2^6 = 64

Therefore, the equivalent expression is 64.