Question

Simplify the expression

${\left(-2f^2{g}^3{h}^2\right)}^3$

Short answer

The simplified version of${\left(-2f^2{g}^3{h}^2\right)}^3$ is $-8f^6{g}^9{h}^6$.

Step-by-step solution

Step 1. State the product power law of ‘laws of indices’. 

According to this law,when a product is raised to a power, every factor of the product is raised to the power.

In general:${\left(xy\right)}^m=x^m{y}^m$

Step 2. State the ‘Law of indices’ for power of index numbers.

If a term with a power is itself raised to a power then the powers are multiplied together.

In general:${\left(x^m\right)}^n=x^{m\times n}$

Step 3. Simplify the expression.

The given expression is:${\left(-2f^2{g}^3{h}^2\right)}^3$

First apply the product power law to simplify the given expression.

${\left(-2f^2{g}^3{h}^2\right)}^3=\left(-2^3\right){\left(f^2\right)}^3{\left(g^3\right)}^3{\left(h^2\right)}^2$

Apply the ‘Law of indices’ for power of index numbers and simplify further.

$$\begin{gathered} {\left(-2f^2{g}^3{h}^2\right)}^3={\left(-2\right)}^3{\left(f^2\right)}^3{\left(g^3\right)}^3{\left(h^2\right)}^3 \\ =\left(-8\right)\left(f^{2\times 3}\right)\left(g^{3\times 3}\right)\left(h^{2\times 3}\right) \\ =\left(-8\right)\left(f^6\right)\left(g^9\right)\left(h^6\right) \\ =-8f^6{g}^9{h}^6 \end{gathered}$$