Solve (4²/7⁴)²: Calculating Powers of Complex Fractions

(4274)2= (\frac{4^2}{7^4})^2=

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Step-by-step video solution

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00:08 Let's simplify.
00:11 We will use a special formula for fraction exponents.
00:15 When a fraction is raised to a power, we need to raise both the top and bottom to that power.
00:22 We'll use this formula in our exercise.
00:26 Next, let's apply the power of a power rule.
00:29 If we have a number A raised to the power of N, then to the power of M,
00:35 we write it as A to the power of the product of exponents, M times N.
00:41 We'll use this rule in our exercise as well.
00:45 Now, let's multiply the exponents and see what we get.
00:49 And that's how we find the solution to our question!

Step-by-step written solution

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1

Understand the problem

(4274)2= (\frac{4^2}{7^4})^2=

2

Step-by-step solution

(4274)2=42×274×2=4478 (\frac{4^2}{7^4})^2=\frac{4^{2\times2}}{7^{4\times2}}=\frac{4^4}{7^8}

3

Final Answer

4478 \frac{4^4}{7^8}

Practice Quiz

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

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