8^ 1× 5^32^ 4 =8^ 1× 5^3×2^4 #160; #160; [a^ b=1a^b] ⇒ 2^ 3×5^3×2^4 #160; #160; #160; #160; #160; [a^b.a^c=a^b+c] ...

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Fractional Exponent

Solve: 8-1× ...

Question

Solve:
$\frac{8^{- 1} \times 5^{3}}{2^{- 4}}$

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Solution

$\frac{8^{- 1} \times 5^{3}}{2^{- 4}} = 8^{- 1} \times 5^{3} \times 2^{4}$ $[a^{- b} = {\frac{1}{a}}^{b}]$
$\Rightarrow 2^{- 3} \times 5^{3} \times 2^{4}$ $[a^{b} . a^{c} = a^{b + c}]$
$\Rightarrow 2^{4 - 3} \times 5^{3}$
$\Rightarrow 2 \times 125 = 250$ .

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