Question

Simplyfy 8 1/3 x 16 1/3 / 32-1/3

Answer 1

Answer:

Value \: of \:\frac{8^{\frac{1}{3}}\times (16)^{\frac{1}{3}}}{(32)^{\frac{-1}{3}}}=16

Step-by-step explanation:

\frac{8^{\frac{1}{3}}\times (16)^{\frac{1}{3}}}{(32)^{\frac{-1}{3}}}

=8^{\frac{1}{3}}\times (16)^{\frac{1}{3}}\times (32)^{\frac{-1}{3}}

/* By Exponential identity:

\boxed { \frac{1}{a^{-n}}=a^{n}}

=\sqrt[3]{8\times 16 \times 32}

=\sqrt[3]{2^{3}\times 2^{4}\times 2^{5}}

=\sqrt[3]{2^{3+4+5}}

=\sqrt[3]{2^{12}}

= 2^{\frac{12}{3}}

/* \boxed {(a^{m})^{n}=a^{mn}}*/

=2^{4}

=16

Therefore,

Value \: of \:\frac{8^{\frac{1}{3}}\times (16)^{\frac{1}{3}}}{(32)^{\frac{-1}{3}}}=16