Calculate (9×10×7)^5: Evaluating Products Raised to Powers

Choose the expression that corresponds to the following:

(9×10×7)5= \left(9\times10\times7\right)^5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Let's simplify this math problem together.
00:13 When multiplying factors with the same exponent, N,
00:17 Raise each factor to the power of N.
00:23 We'll use this rule for our problem.
00:32 Here's the solution!

Step-by-step written solution

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1

Understand the problem

Choose the expression that corresponds to the following:

(9×10×7)5= \left(9\times10\times7\right)^5=

2

Step-by-step solution

We begin by noting that the given expression is (9×10×7)5 \left(9\times10\times7\right)^5 . Our task is to expand this expression using the power of a product rule.

The power of a product rule states that for any real numbers a a , b b , and c c and a positive integer n n , (a×b×c)n=an×bn×cn (a \times b \times c)^n = a^n \times b^n \times c^n .

Applying this rule to the given expression, we set a=9a = 9, b=10b = 10, and c=7c = 7, and n=5n = 5.

By substituting these into the power of a product formula, we have:

  • an=95 a^n = 9^5

  • bn=105 b^n = 10^5

  • cn=75 c^n = 7^5

Therefore, the expression (9×10×7)5 \left(9\times10\times7\right)^5 expands to:

95×105×75 9^5\times10^5\times7^5

3

Final Answer

95×105×75 9^5\times10^5\times7^5

Practice Quiz

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

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