Solve 7⁴ × 8³ × (1/7)⁴: Power and Reciprocal Multiplication

74⋅83⋅(17)4=? 7^4\cdot8^3\cdot(\frac{1}{7})^4=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's simplify the problem together.
00:15 If a fraction has an exponent, both the top and bottom numbers are raised to that power.
00:24 We'll use this rule for our exercise, so let's get started!
00:30 Now, let's reduce wherever we can.
00:38 Remember, one raised to any power is always one.
00:44 And there you go, that's the solution!

Step-by-step written solution

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1

Understand the problem

74⋅83⋅(17)4=? 7^4\cdot8^3\cdot(\frac{1}{7})^4=\text{?}

2

Step-by-step solution

We use the formula:

(ab)n=anbn (\frac{a}{b})^n=\frac{a^n}{b^n}

We decompose the fraction inside of the parentheses:

(17)4=1474 (\frac{1}{7})^4=\frac{1^4}{7^4}

We obtain:

74×83×1474 7^4\times8^3\times\frac{1^4}{7^4}

We simplify the powers: 74 7^4

We obtain:

83×14 8^3\times1^4

Remember that the number 1 in any power is equal to 1, thus we obtain:

83×1=83 8^3\times1=8^3

3

Final Answer

83 8^3

Practice Quiz

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Which of the following is equivalent to \( 100^0 \)?

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