Calculate the Square of 4/7: Evaluating (4/7)²

Q: Is there a shortcut for squaring fractions?

Yes! Use the rule $ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} $. For squaring, just remember: square the top, square the bottom.

Q: What if I get confused about which number goes where?

Write it out step by step: $ \left(\frac{4}{7}\right)^2 = \frac{4^2}{7^2} = \frac{16}{49} $. The exponent applies to both numerator and denominator separately.

Fraction Exponents with Squared Terms

Insert the corresponding expression:

$\left(\frac{4}{7}\right)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the following problem

00:03 According to the laws of exponents, a fraction raised to the power (N)

00:07 equals the numerator and denominator, each raised to the same power (N)

00:12 We will apply this formula to our exercise

00:18 Let's calculate each power and substitute accordingly

00:29 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\left(\frac{4}{7}\right)^2=$

Step-by-step solution

To solve the problem of squaring the fraction $\left(\frac{4}{7}\right)^2$ , we will follow these steps:

Step 1: Determine the square of the numerator. The numerator is $4$ , and $4^2 = 16$ .
Step 2: Determine the square of the denominator. The denominator is $7$ , and $7^2 = 49$ .
Step 3: Combine these results to form the fraction $\frac{16}{49}$ .

The computation involves squaring both the numerator and the denominator separately. In conclusion, the squared fraction is:

$\frac{16}{49}$

Therefore, the corresponding expression for $\left(\frac{4}{7}\right)^2$ is $\frac{16}{49}$ .

Final Answer

$\frac{16}{49}$

Key Points to Remember

Essential concepts to master this topic

Rule: Square both numerator and denominator separately when raising fractions to powers
Technique: Calculate $4^2 = 16$ and $7^2 = 49$ to get $\frac{16}{49}$
Check: Verify $\frac{4}{7} \times \frac{4}{7} = \frac{16}{49}$ by multiplying fractions ✓

Common Mistakes

Avoid these frequent errors

Only squaring the numerator or denominator
Don't square just the numerator 4 to get $\frac{16}{7}$ or just the denominator to get $\frac{4}{49}$ ! This violates the exponent rule and gives completely wrong answers. Always square both the numerator AND denominator: $\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$ .

Practice Quiz

Test your knowledge with interactive questions

$(3\times4\times5)^4=$

FAQ

Everything you need to know about this question

Why do I square both the top and bottom numbers?

When you square a fraction, you're multiplying it by itself: $\left(\frac{4}{7}\right)^2 = \frac{4}{7} \times \frac{4}{7}$ . This means both parts get multiplied, so both need to be squared!

Is there a shortcut for squaring fractions?

Yes! Use the rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ . For squaring, just remember: square the top, square the bottom.

Do I need to simplify my answer?

Always check if your answer can be simplified! In this case, $\frac{16}{49}$ is already in lowest terms since 16 and 49 share no common factors.

What if I get confused about which number goes where?

Write it out step by step: $\left(\frac{4}{7}\right)^2 = \frac{4^2}{7^2} = \frac{16}{49}$ . The exponent applies to both numerator and denominator separately.

How can I check if my answer is right?

Multiply your result by itself using fraction multiplication: $\frac{4}{7} \times \frac{4}{7} = \frac{4 \times 4}{7 \times 7} = \frac{16}{49}$ . This should match your squared answer!

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