Evaluate : (43)½

GIven: $\left(4^{3}\right)^{\frac{1}{2}}$


To do: Simplify the expression

Solution:


$\left(4^{3}\right)^{\frac{1}{2}}$

Apply exponent rule: $\left(a^{b}\right)^{c}=a^{b c}$

$\left(4^{3}\right)^{\frac{1}{2}}=4^{3 \cdot \frac{1}{2}}$

$=4^{3 \cdot \frac{1}{2}}$

$3 \cdot \frac{1}{2}=\frac{3}{2}$

$=4^{\frac{3}{2}}$

Factor the number: $4=2^{2}$

$=\left(2^{2}\right)^{\frac{3}{2}}$

Apply exponent rule: $\left(a^{b}\right)^{c}=a^{b c} $

$\left(2^{2}\right)^{\frac{3}{2}}=2^{2 \cdot \frac{3}{2}}$

$=2^{2 \cdot \frac{3}{2}}$

$2 \cdot \frac{3}{2}=3$

$=2^{3}$

$2^{3}=8$

$=8$
 

Updated on: 10-Oct-2022

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