2m-2n t- 2n-2t m- 2t-2m n is equal to

The correct option is A 1 ( 2^m/2^n )^t× ( 2^n/2^t )^m× ( 2^t/2^m )^n = #160; ( 2^m n )^t× ( 2^n t )^m× ( 2^t m )^n #160;= #160; 2^mt ...

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Byju's Answer

Standard XII

Mathematics

Logarithmic Function

2m/2n t× 2n/2...

Question

${(\frac{2^{m}}{2^{n}})}^{t} \times {(\frac{2^{n}}{2^{t}})}^{m} \times {(\frac{2^{t}}{2^{m}})}^{n}$ is equal to

1

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2

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\frac{1}{2}

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0

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Solution

The correct option is A $1$
${(\frac{2^{m}}{2^{n}})}^{t} \times {(\frac{2^{n}}{2^{t}})}^{m} \times {(\frac{2^{t}}{2^{m}})}^{n}$
= ${(2^{m - n})}^{t} \times {(2^{n - t})}^{m} \times {(2^{t - m})}^{n}$
= $2^{m t - n t} \times 2^{n m - t m} \times 2^{t n - m n}$
= $2^{m t - n t + n m - t m + t n - m n}$
= $2^{0} = 1$

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(2m2n)t×(2n2t)m×(2t2m)n is equal to

The correct option is A 1(2m2n)t×(2n2t)m×(2t2m)n= (2m−n)t×(2n−t)m×(2t−m)n = 2mt−nt×2nm−tm×2tn−mn= 2mt−nt+nm−tm+tn−mn= 20=1

${(\frac{2^{m}}{2^{n}})}^{t} \times {(\frac{2^{n}}{2^{t}})}^{m} \times {(\frac{2^{t}}{2^{m}})}^{n}$ is equal to