Question
What integer is equivalent to \( 25^{\frac{3}{2}} \) ?
Ask by Rodriguez Powers. in the United States
Jan 19,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The integer equivalent of \( 25^{\frac{3}{2}} \) is **125**.
Solution
To find the integer equivalent of \( 25^{\frac{3}{2}} \), follow these steps:
1. **Understand the Exponent:**
The expression \( 25^{\frac{3}{2}} \) can be interpreted as the square root of 25 raised to the power of 3. This is based on the property of exponents:
\[
a^{\frac{m}{n}} = \left( \sqrt[n]{a} \right)^m
\]
2. **Calculate the Square Root:**
\[
\sqrt{25} = 5
\]
3. **Raise the Result to the Power of 3:**
\[
5^3 = 5 \times 5 \times 5 = 125
\]
So, the integer equivalent of \( 25^{\frac{3}{2}} \) is **125**.
**Answer:** 125
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the integer equivalent to \( 25^{\frac{3}{2}} \), we can break this expression down. First, notice that \( 25 \) can be expressed as \( 5^2 \). Therefore: \[ 25^{\frac{3}{2}} = (5^2)^{\frac{3}{2}} = 5^{2 \cdot \frac{3}{2}} = 5^3 \] Now calculating \( 5^3 \): \[ 5^3 = 5 \times 5 \times 5 = 125 \] So, the integer equivalent to \( 25^{\frac{3}{2}} \) is \( 125 \).
