write the following as powers of 2,3, or 5. 2/2^-3

To write \(\frac{2}{2^{-3}}\) as a power of 2, 3, or 5, follow these steps:

1. Simplify the expression \(\frac{2}{2^{-3}}\):

\[
\frac{2}{2^{-3}} = 2 \times 2^{3} \quad \text{(since dividing by a power is the same as multiplying by the reciprocal)}
\]

2. Combine the powers of 2:

\[
2 \times 2^{3} = 2^{1} \times 2^{3} = 2^{1+3} = 2^{4}
\]

So, \(\frac{2}{2^{-3}}\) written as a power of 2 is \(2^{4}\).

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Here are 8 related questions for further practice:

1. Write \( \frac{5}{5^{-2}} \) as a power of 5.
2. Write \( \frac{3}{3^{-4}} \) as a power of 3.
3. Write \( \frac{2^{3}}{2^{5}} \) as a power of 2.
4. Write \( \frac{3^{2}}{3^{-1}} \) as a power of 3.
5. Write \( \frac{5^{3}}{5^{-1}} \) as a power of 5.
6. Write \( \frac{8}{2^{-2}} \) as a power of 2.
7. Write \( \frac{1}{2^{-3}} \) as a power of 2.
8. Write \( \frac{1}{3^{-2}} \) as a power of 3.

**Tip:** When dividing exponents with the same base, subtract the exponent in the denominator from the exponent in the numerator. For example, \(a^m / a^n = a^{m-n}\).

Learn how to write the expression 2 divided by 2 to the power of negative 3 as a power of 2. Understand the power of a power rule and how to simplify fractional exponents step-by-step. Suitable for Grades 9-12.

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