Question

Simplify the following expression.

$(8p^{-3}{)}^{2/3}\times (4p^2{)}^{3/2}÷p^{-3}$ and find the power of $p$

Answer 1

We have,

$(8p^{-3}{)}^{2/3}\times (4p^2{)}^{3/2}÷p^{-3}$

$\frac{(8p^{-3}{)}^{2/3}\times (4p^2{)}^{3/2}}{p^{-3}}$

$\Rightarrow (2^3\times p^{-3}{)}^{2/3}\times ((2p{)}^2{)}^{3/2}\times p^3$

$\Rightarrow (2\times p^{-1}{)}^2\times (2p{)}^3\times p^3$

$\Rightarrow (4\times p^{-2})\times 8p^3\times p^3$

$\Rightarrow (32\times p^{-2})\times p^6$

$\Rightarrow (32\times p^{-2+6})$

$\Rightarrow 32\times p^4$

So, the power of $p$ is $4$.

Hence, this is the answer.