What is the value of [tex][tex]$49^{\frac{3}{2}}$[/tex][/tex]?

Give your answer as a whole number or as a fraction in its simplest form.



Answer :

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]