Question
Simplify the following:$\left(27 \times x^9\right)^{\frac{2}{3}}$
✓
Answer
$\left(27 \times x{^ 9}\right)^{\frac{2}{3}}$
$=\left(3^3 \times x^9\right)^{\frac{2}{3}} $
$ =\left(3^3\right)^{\frac{2}{3}}\left(x^9\right)^{\frac{2}{3}} \ldots \ldots($ Using $( a \times b )^n=a^n \times b^n) $
$=(3)^{3 \times \frac{2}{3}}(\times)^{9 \times \frac{2}{3}} \ldots . .($ Using $\left(a^m\right)^n=a^{m n}) $
$ =(3)^2 x^{3\times 2}$
$=9 x^6 .$
$=\left(3^3 \times x^9\right)^{\frac{2}{3}} $
$ =\left(3^3\right)^{\frac{2}{3}}\left(x^9\right)^{\frac{2}{3}} \ldots \ldots($ Using $( a \times b )^n=a^n \times b^n) $
$=(3)^{3 \times \frac{2}{3}}(\times)^{9 \times \frac{2}{3}} \ldots . .($ Using $\left(a^m\right)^n=a^{m n}) $
$ =(3)^2 x^{3\times 2}$
$=9 x^6 .$
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