Question

find

I. (32)½
ii. (16)¾
​

Answer 1

Answer:

1 -

$= \sf{(32)}^{(\frac{1}{2})}$

$=\sf{(2^5)}^{(\frac{1}{2})}$

$= \sf{(2)^{\frac{5}{2}}}$

$= \sf{(\sqrt2)}^{(5)}$

$= \sf{4√2}$

2 -

$= \sf{(16)}^{(\frac{3}{4})}$

$= \sf{(2^4)}^{(\frac{3}{4})}$

$= \sf{2^3}$

$= \sf{8}$

Answer 2

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{ {32}^{ \frac{1}{2} } } \\ &\sf{ {(16)}^{ \frac{3}{4} } }  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

$\bf \:\large \red{AηsωeR : i.} ✍$

$\tt \:  ⟼ \: {32}^{ \frac{1}{2} }$

$\tt \:  ⟼ {(2 \times 2 \times 2 \times 2 \times 2)}^{ \frac{1}{2} }$

$\tt \:  ⟼ 2 \times 2 \times {(2)}^{ \frac{1}{2} }$

$\tt \:  ⟼ 4 \sqrt{2}$

$\bf \:\large \red{AηsωeR : ii.} ✍$

$\tt \:  ⟼ {(16)}^{ \frac{3}{4} }$

$\tt \:  ⟼ {(2 \times 2 \times 2 \times 2)}^{ \frac{3}{4} }$

$\tt \:  ⟼ {(2)}^{4 \times \frac{3}{4} }$

$\tt \:  ⟼ {2}^{3}$

$\tt \:  ⟼ 8$