Question
Evaluate$:3^3 \times(243)^{-\frac{2}{3}} \times 9^{-\frac{1}{3}}$
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Answer
$ 3^3 \times(243)^{-\frac{2}{3}} \times 9^{\frac{1}{3}}$
$ =3^3 \times(3 \times 3 \times 3 \times 3 \times 3)^{-\frac{2}{3}} \times(3 \times 3)^{-\frac{1}{3}}$
$ =3^3 \times\left(3^5\right)^{-\frac{2}{3}} \times\left(3^2\right)^{\frac{1}{3}}$
$ =3^3 \times 3^{-\frac{10}{3}} \times 3^{-\frac{2}{3}} \ldots\left[\left(a^m\right)^n=a^{m n}\right]$
$ =3^{3-\frac{10}{3}-\frac{2}{3}} \quad\left[a^m \times a^n \times a^o=a^{m+n+o}\right]$
$ =3^{\frac{9-10-2}{3}}$
$ =3^{\frac{9-12}{3}}$
$ =3^{-\frac{3}{3}}$
$ =3^{-1}$
$ =\frac{1}{3}$
$ =3^3 \times(3 \times 3 \times 3 \times 3 \times 3)^{-\frac{2}{3}} \times(3 \times 3)^{-\frac{1}{3}}$
$ =3^3 \times\left(3^5\right)^{-\frac{2}{3}} \times\left(3^2\right)^{\frac{1}{3}}$
$ =3^3 \times 3^{-\frac{10}{3}} \times 3^{-\frac{2}{3}} \ldots\left[\left(a^m\right)^n=a^{m n}\right]$
$ =3^{3-\frac{10}{3}-\frac{2}{3}} \quad\left[a^m \times a^n \times a^o=a^{m+n+o}\right]$
$ =3^{\frac{9-10-2}{3}}$
$ =3^{\frac{9-12}{3}}$
$ =3^{-\frac{3}{3}}$
$ =3^{-1}$
$ =\frac{1}{3}$
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