Calculate (6/8)² : Square of a Fraction Problem

Q: Why do I square both the top and bottom numbers?

When you square a fraction, the entire fraction is multiplied by itself. So $ \left(\frac{6}{8}\right)^2 = \frac{6}{8} \times \frac{6}{8} = \frac{6 \times 6}{8 \times 8} $!

Q: Can I simplify the fraction before squaring?

Yes! $ \frac{6}{8} = \frac{3}{4} $, so you could calculate $ \left(\frac{3}{4}\right)^2 = \frac{9}{16} $. But both methods give equivalent results when simplified.

Q: What's the difference between squaring and doubling a fraction?

Squaring means multiplying by itself: $ \left(\frac{6}{8}\right)^2 = \frac{36}{64} $. Doubling means multiplying by 2: $ 2 \times \frac{6}{8} = \frac{12}{8} $. Very different results!

Q: How do I know which answer choice is correct?

Calculate step-by-step: 6² = 36 and 8² = 64, giving $ \frac{36}{64} $. Then compare exactly with each choice - no need to simplify unless asked!

Q: What if I get confused about the exponent rule?

Remember: $ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} $. The exponent applies to both parts separately. Practice with simple examples like $ \left(\frac{2}{3}\right)^2 = \frac{4}{9} $.

Fraction Powers with Squaring Operations

Insert the corresponding expression:

$\left(\frac{6}{8}\right)^2=$

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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 a power (N)

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

00:11 We'll apply this formula to our exercise

00:20 Let's calculate each power

00:30 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:

$\left(\frac{6}{8}\right)^2=$

Step-by-step solution

To solve this problem, we'll compute $\left(\frac{6}{8}\right)^2$ using the rule for powers of a fraction:

Step 1: Identify the numerator and denominator: $a = 6$ and $b = 8$ .
Step 2: Apply the formula $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ with $n = 2$ .
Step 3: Calculate $a^n = 6^2$ .
Step 4: Calculate $b^n = 8^2$ .

Now, let's carry out the calculations:

Step 3: $6^2 = 36$ .

Step 4: $8^2 = 64$ .

Therefore, $\left(\frac{6}{8}\right)^2 = \frac{36}{64}$ .

We compare $\frac{36}{64}$ with the given answer choices:

Choice 1: $\frac{12}{16}$ is not equal.
Choice 2: $\frac{6}{64}$ is not equal.
Choice 3: $\frac{36}{64}$ matches our result.
Choice 4: $\frac{36}{8}$ is not equal.

Therefore, the correct answer is $\frac{36}{64}$ , which matches Choice 3.

Final Answer

$\frac{36}{64}$

Key Points to Remember

Essential concepts to master this topic

Rule: When squaring fractions, square both numerator and denominator separately
Technique: Apply ( $\frac{a}{b}$ )² = $\frac{a²}{b²}$ , so 6² = 36 and 8² = 64
Check: Verify $\frac{36}{64}$ by confirming 6² = 36 and 8² = 64 ✓

Common Mistakes

Avoid these frequent errors

Adding the exponent to numerator and denominator instead of applying it
Don't just add 2 to get $\frac{8}{10}$ = wrong answer! This ignores the exponent rule completely. Always square each part: ( $\frac{6}{8}$ )² means 6² in numerator and 8² in denominator.

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, the entire fraction is multiplied by itself. So $\left(\frac{6}{8}\right)^2 = \frac{6}{8} \times \frac{6}{8} = \frac{6 \times 6}{8 \times 8}$ !

Can I simplify the fraction before squaring?

Yes! $\frac{6}{8} = \frac{3}{4}$ , so you could calculate $\left(\frac{3}{4}\right)^2 = \frac{9}{16}$ . But both methods give equivalent results when simplified.

What's the difference between squaring and doubling a fraction?

Squaring means multiplying by itself: $\left(\frac{6}{8}\right)^2 = \frac{36}{64}$ . Doubling means multiplying by 2: $2 \times \frac{6}{8} = \frac{12}{8}$ . Very different results!

How do I know which answer choice is correct?

Calculate step-by-step: 6² = 36 and 8² = 64, giving $\frac{36}{64}$ . Then compare exactly with each choice - no need to simplify unless asked!

What if I get confused about the exponent rule?

Remember: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ . The exponent applies to both parts separately. Practice with simple examples like $\left(\frac{2}{3}\right)^2 = \frac{4}{9}$ .

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