How do you simplify ${(2 t)}^{5}$ $(2t)^5$ ?

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How do you simplify ${(2 t)}^{5}$ $(2t)^5$ ?

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Answer 1 · 2016-06-22T01:31:29

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

Explanation:

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

Lets verify using 3 as x
${(2 (3))}^{5} = 32 {(3)}^{5}$ $(2(3))^5 = 32(3)^5$
$6^{5} = 32 (243)$ $6^5=32(243)$
$7776 = 7776$ $7776=7776$
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:
${(4 t x)}^{3} = 4^{3} t^{3} x^{3} = 64 t^{3} x^{3}$ $(4tx)^3 = 4^3t^3x^3 = 64t^3x^3$

I hope you understand power of a product now.

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How do you simplify ${(2 t)}^{5}$ $(2t)^5$ ?

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