Calculate (2×11)^5: Evaluating Powers of Products

Choose the expression that corresponds to the following:

(2×11)5= \left(2\times11\right)^5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's simplify the expression together.
00:14 To open parentheses with an exponent, especially when there's multiplication involved,
00:20 we raise each factor inside to the power separately.
00:24 We'll apply this formula to solve our problem.
00:32 And here is how we find the solution. Great job!

Step-by-step written solution

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1

Understand the problem

Choose the expression that corresponds to the following:

(2×11)5= \left(2\times11\right)^5=

2

Step-by-step solution

To solve the expression, we can apply the rule for the power of a product, which states that(a×b)n=an×bn \left(a \times b\right)^n = a^n \times b^n .

In this case, our expression is (2×11)5 \left(2\times11\right)^5 , wherea=2 a = 2 and b=11 b = 11 , and n=5 n = 5 .

Applying the power of a product rule gives us:

  • an=25 a^n = 2^5

  • bn=115 b^n = 11^5

Therefore, (2×11)5=25×115 \left(2\times11\right)^5 = 2^5 \times 11^5 .

3

Final Answer

25×115 2^5\times11^5

Practice Quiz

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\( 112^0=\text{?} \)

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