Calculate (7/5)² : Squaring a Specific Fraction

Q: Can I just multiply 7×5 and get the answer?

No! That would give you $\frac{35}{25}$, which is wrong. You must square each part separately: numerator squared over denominator squared.

Q: How do I check if my answer is simplified?

Look for common factors in $\frac{49}{25}$. Since 49 = 7×7 and 25 = 5×5, they share no common factors, so this fraction is already in lowest terms!

Q: What if the original fraction wasn't in lowest terms?

Always simplify first before squaring when possible! It makes the calculations easier. For example, $(\frac{6}{4})^2$ is easier as $(\frac{3}{2})^2 = \frac{9}{4}$.

Fraction Exponents with Squared Terms

What is the result of:

$(\frac{7}{5})^2=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the result of:

$(\frac{7}{5})^2=$

Step-by-step solution

To determine $(\frac{7}{5})^2$ , raise both the numerator and the denominator to the power of 2:

Numerator: $7^2 = 7 \times 7 = 49$

Denominator: $5^2 = 5 \times 5 = 25$

Therefore, $(\frac{7}{5})^2 = \frac{49}{25}$ .

Final Answer

$\frac{49}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: When squaring fractions, square both numerator and denominator separately
Technique: $(\frac{7}{5})^2 = \frac{7^2}{5^2} = \frac{49}{25}$
Check: Verify that $\frac{49}{25} \times 1 = \frac{49}{25}$ matches our result ✓

Common Mistakes

Avoid these frequent errors

Adding the exponent to numerator and denominator instead of multiplying
Don't calculate $(\frac{7}{5})^2$ as $\frac{7+2}{5+2} = \frac{9}{7}$ ! This confuses addition with exponentiation and gives a completely wrong result. Always apply the exponent by multiplying: $7^2 = 7 \times 7 = 49$ and $5^2 = 5 \times 5 = 25$ .

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: $(\frac{7}{5})^2 = \frac{7}{5} \times \frac{7}{5}$ . This means both the numerator and denominator get multiplied by themselves.

Can I just multiply 7×5 and get the answer?

No! That would give you $\frac{35}{25}$ , which is wrong. You must square each part separately: numerator squared over denominator squared.

How do I check if my answer is simplified?

Look for common factors in $\frac{49}{25}$ . Since 49 = 7×7 and 25 = 5×5, they share no common factors, so this fraction is already in lowest terms!

What if the original fraction wasn't in lowest terms?

Always simplify first before squaring when possible! It makes the calculations easier. For example, $(\frac{6}{4})^2$ is easier as $(\frac{3}{2})^2 = \frac{9}{4}$ .

Why is my calculator giving me a decimal?

Calculators often convert fractions to decimals automatically. $\frac{49}{25} = 1.96$ , but for math class, leave your answer as a fraction unless told otherwise!

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