Solve (3^5)^4: Evaluating Nested Exponent Expression

(35)4= (3^5)^4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's simplify.
00:10 We will use the formula for power of a power.
00:13 When we have a number, A, raised to the power of N, and then to the power of M.
00:20 We write the base, A, to the power of the product of the exponents, M times N.
00:27 We'll use this formula in our exercise now.
00:31 We'll multiply the powers and find the answer.
00:34 And that's how we solve this question!

Step-by-step written solution

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1

Understand the problem

(35)4= (3^5)^4=

2

Step-by-step solution

To solve the exercise we use the power property:(an)m=an⋅m (a^n)^m=a^{n\cdot m}

We use the property with our exercise and solve:

(35)4=35×4=320 (3^5)^4=3^{5\times4}=3^{20}

3

Final Answer

320 3^{20}

Practice Quiz

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Insert the corresponding expression:

\( \left(10^3\right)^3= \)

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