which of the following is an equivalent expression to 15^0∙7^-2/(-4)^-3

Question

only positive exponents that has been generated

A. 7^2/(-4)^3
B. 4^3/7^2
C. 1/7^2 ∙ (-4)^-3
D. (-4)^3/7^2

Answer 1

To simplify the expression, we can apply the rules of exponents.

First, any number raised to the power of 0 is equal to 1. So, 15^0 is equal to 1.

Next, when we have a negative exponent, we can switch the base and the exponent to make it positive. So, 7^(-2) is equal to 1/7^2.

Similarly, (-4)^(-3) can be rewritten as 1/(-4)^3.

With these simplifications, the expression becomes:

1 * (1/7^2) / (1/(-4)^3)

Next, when we divide by a fraction, we can multiply by its reciprocal. So, dividing by 1/7^2 is the same as multiplying by 7^2.

Now the expression looks like this:

1 * (1/7^2) * 7^2 * (1/(-4)^3)

Next, when we multiply powers with the same base, we add their exponents. So, 7^2 * 7^2 is equal to 7^(2+2) = 7^4.

Similarly, (-4)^3 is equal to -4^(3).

Now the expression becomes:

1 * (1/7^2) * 7^4 * (1/(-4)^3)

Finally, we can combine the fractions by multiplying numerator with numerator and denominator with denominator. So, the expression simplifies to:

(1 * 1 * 7^4) / (7^2 * (-4)^3)

This can be further simplified as:

7^4 / 7^2 * (-4)^3

When dividing like bases with different exponents, we subtract the exponents. So, 7^4 / 7^2 is equal to 7^(4-2) = 7^2.

Now the expression is:

7^2 * (-4)^3

To summarize, the equivalent expression to 15^0 * 7^(-2) / (-4)^(-3) with only positive exponents is option A. 7^2/(-4)^3.