Question
Evaluate the following:$9^4 \div 27^{-\frac{2}{3}}$
✓
Answer
$9^4 \div 27^{-\frac{2}{3}} $
$=\left[(3)^2\right]^4 \div\left[(3)^3\right]^{-\frac{2}{3}}$
$ =(3)^{2 \times 4} \div(3)^{3 \times}\left(-\frac{2}{3}\right) \quad \ldots \ldots($ Using $\left(a^m\right)^n=a^{m n}) $
$=(3)^8 \div(3)-2$
$=(3)^{8-(-2)} \ldots . .($ Using $a^m \div a^n=a^{m-n}) $
$ =(3)^{8+2} $
$ =3^{10}$
$ =(3)^{2 \times 5} $
$ =\left[(3)^2\right]^5$
$=[9]^5 $
$=59049 .$
$=\left[(3)^2\right]^4 \div\left[(3)^3\right]^{-\frac{2}{3}}$
$ =(3)^{2 \times 4} \div(3)^{3 \times}\left(-\frac{2}{3}\right) \quad \ldots \ldots($ Using $\left(a^m\right)^n=a^{m n}) $
$=(3)^8 \div(3)-2$
$=(3)^{8-(-2)} \ldots . .($ Using $a^m \div a^n=a^{m-n}) $
$ =(3)^{8+2} $
$ =3^{10}$
$ =(3)^{2 \times 5} $
$ =\left[(3)^2\right]^5$
$=[9]^5 $
$=59049 .$
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