If a -1 and b -2- then a b - b a - b -2 a -A- 2-2

The correct option is B 1/8Given, a = 1 and b = 2. Then, a^b × b^a=( 1)^2 × (2)^ 1 = 1 ×1/2^1 = 1/2, (∵ a^ m=1/a^m) b 2a = 2 2( 1) = 4. ∴a^b × b^a/b 2a = ...

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Standard VII

Mathematics

Powers with Negative Exponents

If a =-1 and ...

Question

If $a = - 1$ and $b = 2,$ then $\frac{a^{b} \times b^{a}}{b - 2 a}$ = ___.

\frac{3}{4}

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\frac{2}{3}

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\frac{1}{8}

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\frac{1}{4}

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Solution

The correct option is C $\frac{1}{8}$
Given, $a = - 1$ and $b = 2.$
Then, $a^{b} \times b^{a} = (- 1)^{2} \times (2)^{- 1} = 1 \times \frac{1}{2^{1}} = \frac{1}{2}, (∵ a^{- m} = \frac{1}{a^{m}})$
$b - 2 a = 2 - 2 (- 1) = 4.$
$∴ \frac{a^{b} \times b^{a}}{b - 2 a} = \frac{\frac{1}{2}}{4} = \frac{1}{8}$

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If a=−1 and b=2, then ab×bab−2a = ___.

The correct option is C 18Given, a=−1 and b=2. Then, ab×ba=(−1)2×(2)−1=1×121=12, (∵a−m=1am) b−2a=2−2(−1)=4. ∴ab×bab−2a=124=18

If $a = - 1$ and $b = 2,$ then $\frac{a^{b} \times b^{a}}{b - 2 a}$ = ___.