Solve (2×7×3)^(-3): Negative Exponent Expression Problem

Insert the corresponding expression:

(2×7×3)3= \left(2\times7\times3\right)^{-3}=

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Step-by-step video solution

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00:00 Simplify the following problem
00:03 In order to open parentheses with a multiplication operation and an outside exponent
00:09 We'll raise each factor to the power
00:15 We'll apply this formula to our exercise
00:23 This is the solution

Step-by-step written solution

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1

Understand the problem

Insert the corresponding expression:

(2×7×3)3= \left(2\times7\times3\right)^{-3}=

2

Step-by-step solution

To solve the expression (2×7×3)3(2 \times 7 \times 3)^{-3}, let's proceed with the following steps:

Step 1: Recognize that we have a product inside the parentheses, 2×7×32 \times 7 \times 3, which is raised to the power of 3-3.

Step 2: Apply the power of a product rule, which states that (a×b×c)n=an×bn×cn(a \times b \times c)^n = a^n \times b^n \times c^n. This gives us:

(2×7×3)3=23×73×33 (2 \times 7 \times 3)^{-3} = 2^{-3} \times 7^{-3} \times 3^{-3}

Therefore, applying the exponent rule, we have:

23×73×33 2^{-3} \times 7^{-3} \times 3^{-3}

3

Final Answer

23×73×33 2^{-3}\times7^{-3}\times3^{-3}

Practice Quiz

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

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