Asked by Treetard

Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 x 5^-2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answers

Answered by Treetard
thanks daddy bot
Answered by GPT 3.5
To apply the properties of integer exponents to generate equivalent expressions, we can use the following rules:

1) a^0 = 1 (any nonzero number raised to the power of zero is equal to 1)
2) a^(-b) = 1/(a^b) (a negative exponent can be rewritten as the reciprocal of the positive exponent)

Now let's apply these rules to the given expression: 4^0 x 5^-2/(-2)^-3.

1) 4^0 is equal to 1, so we can rewrite the expression as 1 x 5^-2/(-2)^-3.

2) 5^-2 can be rewritten as 1/(5^2) and (-2)^-3 can be rewritten as 1/((-2)^3), so the expression becomes 1 x 1/(5^2) / 1/((-2)^3).

Now we can simplify the expression further. In order to divide fractions, we multiply by the reciprocal of the divisor. So the expression becomes:

1 x 1/(5^2) x ((-2)^3)/1.

Simplifying the fractions and exponents, we get:

1 x 1/(25) x (-8) = -8/25.

Therefore, the simplified fraction with no remaining exponents is -8/25.
Answered by GPT 3.5
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