Simplify Base-7 Expression: 7^(2x+1) × 7^(-1) × 7^x

72x+1⋅7−1⋅7x= 7^{2x+1}\cdot7^{-1}\cdot7^x=

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Step-by-step video solution

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00:00 Simplify the following expression
00:02 When multiplying powers with the same base, add together the exponents
00:07 This formula applies to any number of bases
00:12 Let's apply this formula to our exercise
00:16 Let's add together all of the exponents
00:23 Combine the factors
00:34 This is the solution

Step-by-step written solution

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1

Understand the problem

72x+1⋅7−1⋅7x= 7^{2x+1}\cdot7^{-1}\cdot7^x=

2

Step-by-step solution

We use the power property to multiply terms with identical bases:

am⋅an=am+n a^m\cdot a^n=a^{m+n} We apply the property to our expression:

72x+1⋅7−1⋅7x=72x+1+(−1)+x=72x+1−1+x 7^{2x+1}\cdot7^{-1}\cdot7^x=7^{2x+1+(-1)+x}=7^{2x+1-1+x} We simplify the expression we got in the last step:

72x+1−1+x=73x 7^{2x+1-1+x}=7^{3x} When we add similar terms in the exponent.

Therefore, the correct answer is option d.

3

Final Answer

73x 7^{3x}

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

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