Question

hich expression is equivalent to 5^−3/2^−2
written with only positive exponents?

Answer 1

To write the expression \( 5^{-3}/2^{-2} \) with only positive exponents, we can utilize the rule that states \( a^{-n} = \frac{1}{a^n} \).

Here's how we can rewrite the expression:

1. Rewrite each term with positive exponents:
\[
5^{-3} = \frac{1}{5^3}
\]
\[
2^{-2} = \frac{1}{2^2}
\]

2. Substitute these into the original expression:
\[
\frac{5^{-3}}{2^{-2}} = \frac{\frac{1}{5^3}}{\frac{1}{2^2}}
\]

3. Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{1}{5^3}}{\frac{1}{2^2}} = \frac{1}{5^3} \cdot \frac{2^2}{1} = \frac{2^2}{5^3}
\]

4. Then, simplify \( 2^2 \) to \( 4 \):
\[
\frac{2^2}{5^3} = \frac{4}{5^3}
\]

Thus, the expression \( 5^{-3}/2^{-2} \) written with only positive exponents is:

\[
\frac{4}{5^3}
\]