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

Answer 1

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

First, let's simplify the exponent of 15 and 4 within the parentheses:
15^(-3) = 1/15^3
4^7 = 4^4 x 4^3 = (4^4) x 64 = 256 x 64 = 16384

Now, let's rewrite the expression:
[(1/15^3) x 16384]^(0) / 4^(-3)

Any non-zero number raised to the power of 0 is equal to 1, so we can simplify further:
[1 x 16384] / 4^(-3)

The reciprocal of a number raised to a negative exponent is the same number raised to the positive exponent:
[1 x 16384] / (1 / 4^3)

Now, we can simplify further:
16384 / (1 / 64)

Dividing by a fraction is the same as multiplying by its reciprocal:
16384 x 64

Finally, multiply the numbers:
1048576

Therefore, the equivalent expression is 1048576.