State whether the following statement is true or false.
${(3 x^{2})}^{- 3} - {(x^{9})}^{\frac{2}{3}} = \frac{1}{27}$

True

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False

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Solution

The correct option is A True
$(3 x^{2})^{- 3} \times (x^{9})^{\frac{2}{3}}$

$= (3 x^{2})^{- 3} \times (x)^{\frac{2 \times 9}{3}}$

$= (3 x^{2})^{- 3} \times (x)^{6}$

$= 3^{- 3} x^{- 6} \times x^{6}$

$= 3^{- 3} x^{(- 6 + 6)}$

$= 3^{- 3}$

$= \frac{1}{27}$

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