Question

Simplify (16/81)^3/4 × √100/81

Answer 1

Given :  (16/81)^3/4 × √100/81

To Find :  Simplify

Solution:

Laws of exponents :  

$\begin{align} & {{\text{a}}^{n}}\times {{a}^{-n}}=1\text{ or }{{\text{a}}^{n}}=\frac{1}{{{a}^{n}}} \\ & {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \\ & \frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}} \\ & {{\left( {{a}^{m}} \right)}^{n}}={{\left( {{a}^{n}} \right)}^{m}}={{a}^{mn}} \\ & {{a}^{m}}\times {{b}^{m}}={{\left( ab \right)}^{m}} \\ & \frac{{{a}^{n}}}{{{b}^{n}}}={{\left( \frac{a}{b} \right)}^{n}} \\ & {{a}^{0} = 1$

(16/81)^3/4 × √100/81

16 = 2⁴

81  = 3⁴

Hence (16/81)^3/4  =   ((2/3)⁴)^3/4   =  2³/3³  = 8/27

√100/81  = 10/9  

(8/27 )  * (10/9)

= 80/243

 (16/81)^3/4 × √100/81 =  80/243

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