Sure, let's simplify the expression [tex]\((-3) \times (-2)^3\)[/tex] step-by-step.
1. Deal with the exponent first:
Calculate [tex]\((-2)^3\)[/tex]. When raising [tex]\(-2\)[/tex] to the power of 3, we multiply [tex]\(-2\)[/tex] by itself three times:
[tex]\[
(-2)^3 = (-2) \times (-2) \times (-2)
\][/tex]
Multiply the first two [tex]\((-2)\)[/tex]'s:
[tex]\[
(-2) \times (-2) = 4
\][/tex]
Now, multiply the result by [tex]\(-2\)[/tex] again:
[tex]\[
4 \times (-2) = -8
\][/tex]
So, [tex]\((-2)^3 = -8\)[/tex].
2. Multiply the result by the coefficient:
Now we need to multiply [tex]\(-3\)[/tex] by [tex]\(-8\)[/tex]:
[tex]\[
(-3) \times (-8)
\][/tex]
The product of two negative numbers is a positive number, so:
[tex]\[
(-3) \times (-8) = 24
\][/tex]
So, the simplified result of [tex]\( (-3) \times (-2)^3 \)[/tex] is [tex]\( 24 \)[/tex].
