Express 2-3-4 with postive exponent-

The correct option is B (3/2)^4Since a^m/b^m=(a/b)^m for integers a,m and b (a,b≠ 0), (2/3)^ 4=2^ 4/3^ 4 But, a^ m=1/a^m. nbsp;(2/3)^ 4=2^ 4/3^ 4=1/2^4/1/3^4=3 ...

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Byju's Answer

Standard VIII

Mathematics

Positive and Negative Powers

Express 2/3-4...

Question

Express $(\frac{2}{3})^{- 4}$ with positive exponent.

{(\frac{2}{3})}^{4}

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{(\frac{3}{2})}^{4}

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{(\frac{3}{2})}^{2}

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{(\frac{2}{3})}^{2}

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Solution

The correct option is B ${(\frac{3}{2})}^{4}$
Since $\frac{a^{m}}{b^{m}} = (\frac{a}{b})^{m}$ for integers $a, m$ and $b$ $(a, b \neq 0),$
$(\frac{2}{3})^{- 4} = \frac{2^{- 4}}{3^{- 4}}$
But, $a^{- m} = \frac{1}{a^{m}} .$
$⟹ (\frac{2}{3})^{- 4} = \frac{2^{- 4}}{3^{- 4}} = \frac{\frac{1}{2^{4}}}{\frac{1}{3^{4}}} = \frac{3^{4}}{2^{4}} = (\frac{3}{2})^{4}$

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Express (23)−4 with positive exponent.

The correct option is B (32)4Since ambm=(ab)m for integers a,m and b (a,b≠0), (23)−4=2−43−4 But, a−m=1am. ⟹(23)−4=2−43−4=124134=3424=(32)4

Express $(\frac{2}{3})^{- 4}$ with positive exponent.