Question

((32)^2/5(4)^-1/2(8)^1/3)/(2^-2/(64)^-1/3)

Answer 1

Given :  (( 32)^(2/5) * 4^(-1/2)(8)^(1/3)) /(2⁻²/(64)^(-1/3))

To Find : Simplify

Solution :

 (( 32)^(2/5) * 4^(-1/2)(8)^(1/3)) /(2⁻²/(64)^(-1/3))

32 = 2⁵

32^(2/5)  =   (2⁵)^(2/5) =  2²  = 4

4^(-1/2) =(2²)^(-1/2)   =2⁻¹ = 1/2

8 = 2³

(8)^(1/3) = (2³)^(1/3) = 2¹ = 2

 (( 32)^(2/5) * 4^(-1/2)(8)^(1/3))

= 4 (1/2) 2

= 4

64 = 4³

=> (64)^(-1/3) = ( 4³)(-1/3) = 4⁻¹

2⁻² = 4⁻¹

4⁻¹ / 4⁻¹ = 1

2⁻²/(64)^(-1/3))  = 1

( (32)^(2/5) * 4⁻¹ - (1/2)(8)^(1/3)) /(2⁻²/(64)^(-1/3))

=4/1

= 4

 (( 32)^(2/5) * 4^(-1/2)(8)^(1/3)) /(2⁻²/(64)^(-1/3))  = 4

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Answer 2

$\huge\underline {\sf \green{Answer -}}$

$\sf{ {32}^{ \frac{2}{5} } } \times {4}^{ \frac{ - 1}{2} } \times {8}^{ \frac{1}{3} } ( \frac{ {2}^{ - 2} }{ {64}^{ \frac{ - 1}{3} } } )$

$\sf \implies{( { {2}^{5} )}^{ \frac{2}{5} } } \times ( { {2}^{2} )}^{ \frac{ - 1}{2} } \times ( { {2}^{3}) }^{ \frac{1}{3} } \times ( \frac{ {2}^{ - 2} }{ ( {4}^{3} )^{ - \frac {1}{3} } } ) \\ \\ \sf \implies{{( { {2}^{ \cancel 5} )}^{ \frac{2}{ \cancel5} } } \times ( { {2}^{ \cancel2} )}^{ \frac{ - 1}{ \cancel2} } \times ( { {2}^{ \cancel3}) }^{ \frac{1}{ \cancel3} } \times ( \frac{ {2}^{ - 2} }{ ( {4}^{ \cancel 3} ) ^{ - \frac {1}{ \cancel3} } } )} \\ \\ \sf \implies{ {2}^{2} \times {2}^{ - 1} \times {2}^{1} \times \frac{ {2}^{ - 2} }{ {4}^{ - 1} } } \\ \\ \sf \implies{ {2}^{2} \times \frac{1}{ {2}^{1} } \times 2 \times \frac{ \frac{1}{ {2}^{2} } }{ \frac{1}{ {4}^{1} } } } \\ \\ \sf \implies{4 \times \frac{1}{2} \times 2 \times \frac{ \frac{1}{ 4} }{ \frac{1}{ {4}} } } \\ \\ \sf \implies{4 \times \frac{1}{ \cancel2} \times \cancel2 \times \frac{ \frac{1}{ \cancel4} }{ \frac{1}{ { \cancel4}} } } \\ \\ \sf {\red{ \implies \star \: \: {4} \: \: \: \: \: \: \: \: \: \: \: ....ans}}$