How do you simplify (2t)^5?

Jun 22, 2016

Answer:

Use the power of a product rule that states: $\left(a b\right) x = {a}^{x} {b}^{x}$.
Therefore, ${\left(2 t\right)}^{5} = {2}^{5} {t}^{5} = 32 {t}^{5}$

Explanation:

In your question the $2$ was the $a$, the $t$ was the $b$ and the $5$ was the $x$.

Lets verify using 3 as x
${\left(2 \left(3\right)\right)}^{5} = 32 {\left(3\right)}^{5}$
${6}^{5} = 32 \left(243\right)$
$7776 = 7776$
It works out!

The power of a product rule works for any product and power.
Another example of the product of a power rule is as follows:
${\left(4 t x\right)}^{3} = {4}^{3} {t}^{3} {x}^{3} = 64 {t}^{3} {x}^{3}$

I hope you understand power of a product now.