Question

Simplify the expression the quantity 16 times x to the fourth power end quantity to the one-half power. 4 times x to the power of nine-halves 16 times x to the power of nine-halves 4x2 16x2

Answer 1

Answer:

4x²

Step-by-step explanation:

Given expression:

$\left(16x^4\right)^\frac{1}{2}$

Rewrite 16 as 4²:

$\left(4^2x^4\right)^\frac{1}{2}$

$\textsf{Apply exponent rule} \quad (a^b \cdot c^d)^n=a^{bn} \cdot c^{dn}$

$\implies 4^{2 \cdot \frac{1}{2}} \cdot x^{4 \cdot \frac{1}{2}}$

Simplify:

$\implies 4^{\frac{2}{2}} \cdot x^{\frac{4}{2}}$

$\implies 4^{1} \cdot x^2}$

$\implies 4x^2$