Certainly! Let's break down the computation of [tex]\( 16^{\frac{3}{2}} \)[/tex] step by step:
1. Rewrite the exponent:
The expression [tex]\( 16^{\frac{3}{2}} \)[/tex] can be rewritten using properties of exponents. Specifically, we can write it as [tex]\( (16^{\frac{1}{2}})^3 \)[/tex].
2. Calculate the square root of the base:
The term [tex]\( 16^{\frac{1}{2}} \)[/tex] represents the square root of 16. The square root of 16 is 4, since [tex]\( 4 \times 4 = 16 \)[/tex].
3. Raise the result to the power of 3:
Now that we have evaluated the square root of 16 to be 4, we need to raise this result to the power of 3. This means we need to calculate [tex]\( 4^3 \)[/tex].
4. Perform the final exponentiation:
[tex]\( 4^3 \)[/tex] means [tex]\( 4 \times 4 \times 4 \)[/tex]. Calculating this, we get:
[tex]\[
4 \times 4 = 16
\][/tex]
[tex]\[
16 \times 4 = 64
\][/tex]
Therefore, the value of [tex]\( 16^{\frac{3}{2}} \)[/tex] is [tex]\( 64 \)[/tex].
