Question

simplify
(27x^-3y^6)^2/3​

Answer 1

SOLUTION

TO SIMPLIFY

$\displaystyle \sf{ {(27{x}^{ - 3} {y}^{6} )}^{ \frac{2}{3} } }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\sf{1. \: \: {( {a}^{m} )}^{n} = {a}^{mn} }$

$\sf{2. \: \: {(ab)}^{n} = {a}^{n} \times {b}^{n} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ {(27{x}^{ - 3} {y}^{6} )}^{ \frac{2}{3} } }$

Now we simplify it as below

$\displaystyle \sf{ = {(27)}^{ \frac{2}{3} } \times {({x}^{ - 3} )}^{ \frac{2}{3} } \times {( {y}^{6} )}^{ \frac{2}{3} } } \: \: \: (by \: formula \: 2)$

$\displaystyle \sf{ = {( {3}^{3} )}^{ \frac{2}{3} } \times {({x}^{ - 3} )}^{ \frac{2}{3} } \times {( {y}^{6} )}^{ \frac{2}{3} } }$

$\displaystyle \sf{ = {( 3 )}^{ 3 \times \frac{2}{3} } \times {(x )}^{ - 3 \times \frac{2}{3} } \times {( y)}^{ 6 \times \frac{2}{3} } } \: \: \: \: (by \: formula \: 1)$

$\displaystyle \sf{ = {( 3 )}^{ 2} \times {(x )}^{ - 2} \times {( y)}^{ 2 \times 2 }}$

$\displaystyle \sf{ = 9 \times {x}^{ - 2} \times {y}^{ 4}}$

$\displaystyle \sf{ = 9 {x}^{ - 2} {y}^{ 4}}$

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