Application of laws of exponents based on numerical powers
simplify:

(i) $2^{\frac{3}{2}} 2^{\frac{1}{5}}$
(ii) ${(\frac{1}{3^{3}})}^{7}$

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Solution

(i) $2^{\frac{3}{2}} \cdot 2^{\frac{1}{5}}$

We know that, $(a^{m} a^{n} = a^{m + n})$

$\Rightarrow 2^{\frac{3}{2} + \frac{1}{5}} = 2^{\frac{17}{10}}$

(ii) ${(\frac{1}{3^{3}})}^{7}$

$\Rightarrow \frac{1}{(3^{3})^{7}} = \frac{1}{3^{21}}$ $((a^{m})^{n} = a^{m n})$ .

$∴ 2^{\frac{3}{2}} \cdot 2^{\frac{1}{5}} = 2^{\frac{17}{10}}$

and ${(\frac{1}{3^{3}})}^{7} = \frac{1}{3^{21}}$

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2^{2 x + 1} = 8

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