Q2. Simplify and express the result in power notation with positive exponent.    (ii) $\left (\frac{1}{2^3} \right )^2$

M manish

The detailed solution for the above-written question is as follows

We know the exponential formula

$\frac{a^{m}}{b^{m}} = (\frac{a}{b})^{m}$        and   $a^{-m}= \frac{1}{a^{m}}$  and  $(a^{m})^{n} = a^{mn}$

So, we have given

a = 1, b=2

By using above exponential law,

$\frac{a^{m}}{b^{m}} = \frac{1}{(2^{3})^{2}} = \frac{1}{2^{6}}$

$= \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} = \frac{1}{64}$

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