To find the value of [tex]\( 49^{\frac{3}{2}} \)[/tex], we will proceed step-by-step:
1. Understanding the Exponent [tex]\(\frac{3}{2}\)[/tex]:
- The exponent [tex]\(\frac{3}{2}\)[/tex] can be interpreted as a combination of two operations:
- Squaring the base.
- Taking the square root of the base.
2. Rewriting the Expression:
- The expression [tex]\( 49^{\frac{3}{2}} \)[/tex] can be written as [tex]\( (49^{\frac{1}{2}})^3 \)[/tex] or [tex]\( \sqrt{49}^3 \)[/tex].
3. Calculating the Square Root:
- First, calculate the square root of 49:
[tex]\[
\sqrt{49} = 7
\][/tex]
4. Raising to the Power of 3:
- Next, raise 7 to the power of 3:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
Thus, the value of [tex]\( 49^{\frac{3}{2}} \)[/tex] is [tex]\( 343 \)[/tex].
So, the final answer is:
[tex]\[
49^{\frac{3}{2}} = 343
\][/tex]
