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

Question

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

Video Solution

Solution Steps

00:00 Simplify the expression
00:02 When multiplying powers with the same base, add the exponents
00:07 This formula applies to any number of bases
00:12 Let's use this formula in our exercise
00:16 Let's sum all the exponents
00:23 Let's group the factors
00:34 And this is the solution to the question

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.

Answer

73x 7^{3x}

More Questions

Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Multiplying Exponents with the Same Base

Question Types

Applying Combined Exponents Rules: Variables in the exponent of the power Multiplication of Powers: Variables in the exponent of the power