Select all of the expressions that are equivalent to 5^3/5^−2

Question

Responses

55
5 to the th power5

3125
3125

15
over1

5−1
5 inverse

51
5 to the th power1

5

Answer 1

To simplify the expression \( \frac{5^3}{5^{-2}} \), we can use the properties of exponents. According to the rules of exponents, when you divide with the same base, you subtract the exponents:

\[ \frac{5^3}{5^{-2}} = 5^{3 - (-2)} = 5^{3 + 2} = 5^5 \]

Now we will evaluate the responses to see which are equivalent to \( 5^5 \):

1. 55 - This is not equivalent to \( 5^5 \).
2. 5 to the th power5 - This is equivalent to \( 5^5 \).
3. 3125 - \( 5^5 = 3125 \). So this is equivalent.
4. 15 over 1 - This simplifies to 15, which is not equivalent to \( 5^5 \).
5. 5^-1 - This is not equivalent since it represents \( \frac{1}{5} \).
6. 5 to the th power1 - This is \( 5^1 \), which is not equivalent to \( 5^5 \).
7. 5 - This is not equivalent as it represents \( 5^1 \).

The expressions that are equivalent to \( \frac{5^3}{5^{-2}} \) are:

• 5 to the th power5
• 3125