Question

How do you multiply ${\left(-5x^4{y}^2\right)}^3$.

Answer 1

Simplifying ${\left(-5x^4{y}^2\right)}^3$:

It is a rule of simplifying expressions involving powers of the same base number.

From the reference of the Index law we know that,

${\left(a^m\right)}^n=a^{mn}$

Since, we have to multiply all the powers of the values within the bracket by $3$ thus.

$$\begin{gathered} {\left(-5x^4{y}^2\right)}^3={\left(-5^1\right)}^3\times {\left(x^4\right)}^3\times {\left(y^2\right)}^3 \\ ={\left(-5\right)}^{1\times 3}\times {\left(x\right)}^{4\times 3}\times y^{2\times 3} \\ ={\left(-5\right)}^3\times {\left(x\right)}^{12}\times y^6 \\ =-125x^{12}{y}^6 \end{gathered}$$

Therefore, the value of ${\left(-5x^4{y}^2\right)}^3$ is $-125x^{12}{y}^6$.