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?

Question

a. 1/64
b. 64
c. 60/4^-3
d. 1 x 4^-3

Answer 1

To simplify this expression, let's apply the properties of integer exponents.

First, let's simplify the expression inside the parentheses:
(15^-3 x 4^7) = (1/15^3 x 4^7) = (1/3375 x 16384)

Now, let's simplify the expression outside the parentheses:
(1/3375 x 16384)^0 = 1

Finally, let's simplify the expression with the negative exponent:
4^-3 = 1/4^3 = 1/64

Putting it all together:
(15^-3 x 4^7)^0 / 4^-3 = 1/1 / 1/64 = 64

Therefore, the equivalent expression is option b. 64.