Question

Apply the Properties of integer exponents to generate an equivalent expression to 4^0x5^(-2)/(-2)^(-3) with only positive exponents, then solve the expression. As a simplified fraction.

Answer 1

To generate an equivalent expression with only positive exponents, we can apply the following properties of integer exponents:

1. Any non-zero number raised to the power of 0 is equal to 1: a^0 = 1 (where a is a non-zero number)
2. The reciprocal of a number raised to a negative exponent is equal to the number raised to the positive exponent in the denominator: a^(-n) = 1/(a^n)

Let's apply these properties step by step to simplify the expression:

First, using property 1, we have:
4^0 = 1

Now, let's apply property 2 to simplify the expression further:
5^(-2) = 1/(5^2) = 1/25
(-2)^(-3) = 1/((-2)^3) = 1/(-8) = -1/8

Now, substituting these simplified values back into the expression, we have:
1x(1/25)/( -1/8 )

Simplifying further, we have:
(1/25) × (-8/-1) = 8/25

Therefore, the simplified fraction equivalent to the expression 4^0x5^(-2)/(-2)^(-3) is 8/25.