Question

Evaluate: $(-4)\times {(-4)}^2$

Answer 1

Hint: We know the law of exponents that is powers with same base: $x^a\times x^b=x^{a+b}$

And

$$\begin{gathered} {(-a)}^n={\left(a\right)}^{n}ifniseven \\ =-{\left(a\right)}^{n}ifnisodd \end{gathered}$$

Step 1: Given expression: $(-4)\times {(-4)}^2$

Step2: Solution:

Form the above criteria of law of exponents:

$$\begin{gathered} (-4)\times {(-4)}^2={(-4)}^{1+2}\{U\sin g{x}^a\times x^b=x^{a+b}\} \\ ={(-4)}^3 \\ =-64\{As3isodd\} \end{gathered}$$

$-64$, This is the required value.

Final Answer: $-64$, This is the required value.