How do you simplify #(2t)^5#?

1 Answer
Dylan D.
Jun 22, 2016

Use the power of a product rule that states: #(ab)x=a^xb^x#.
Therefore, #(2t)^5=2^5t^5=32t^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
#(2(3))^5 = 32(3)^5#
#6^5=32(243)#
#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:
#(4tx)^3 = 4^3t^3x^3 = 64t^3x^3#

I hope you understand power of a product now.

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