Simplify the Exponential Expression: 5^(2x) × 5^x

Reduce the following equation:

52x×5x= 5^{2x}\times5^x=

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Step-by-step video solution

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00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of powers with equal bases (A)
00:11 equals the same base raised to the sum of the exponents (N+M)
00:15 Let's apply this formula to our exercise
00:19 We'll maintain the base and add together the exponents
00:23 This is the solution

Step-by-step written solution

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1

Understand the problem

Reduce the following equation:

52x×5x= 5^{2x}\times5^x=

2

Step-by-step solution

To reduce the expression 52x×5x 5^{2x} \times 5^x , we will use the exponent multiplication rule:

When multiplying powers with the same base, add the exponents:
Thus, 52x×5x=52x+x 5^{2x} \times 5^x = 5^{2x + x} .

Hence, the correct choice is: 52x+x 5^{2x + x} .

3

Final Answer

52x+x 5^{2x+x}

Practice Quiz

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

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