Evaluate (5/6)² : Calculate the Square of Five-Sixths

Q: Can I simplify the answer further?

Always check if your answer can be simplified! For $\frac{25}{36}$, find the GCD of 25 and 36. Since 25 = 5² and 36 = 6², and they share no common factors, this fraction is already in simplest form.

Q: What if the exponent was 3 instead of 2?

The same rule applies! $(\frac{5}{6})^3 = \frac{5^3}{6^3} = \frac{125}{216}$. Just raise both the numerator and denominator to whatever power is given.

Q: How is this different from adding fractions?

Completely different! Adding fractions requires a common denominator, but raising to a power just means multiplying the fraction by itself. No common denominators needed!

Q: What's the fastest way to check my work?

Use multiplication! $\frac{5}{6} \times \frac{5}{6}$ should equal your answer. Multiply across: $\frac{5 \times 5}{6 \times 6} = \frac{25}{36}$ ✓

Fraction Exponents with Square Powers

Evaluate the expression:

$(\frac{5}{6})^2=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Evaluate the expression:

$(\frac{5}{6})^2=$

Step-by-step solution

To evaluate $(\frac{5}{6})^2$ , raise both the numerator and the denominator to the power of 2:

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

Denominator: $6^2 = 6 \times 6 = 36$

Therefore, $(\frac{5}{6})^2 = \frac{25}{36}$ .

Final Answer

$\frac{25}{36}$

Key Points to Remember

Essential concepts to master this topic

Rule: Square both numerator and denominator separately when raising fractions to powers
Technique: $(\frac{5}{6})^2 = \frac{5^2}{6^2} = \frac{25}{36}$
Check: Multiply $\frac{5}{6} \times \frac{5}{6} = \frac{25}{36}$ to verify ✓

Common Mistakes

Avoid these frequent errors

Adding exponent to numerator and denominator instead of multiplying
Don't calculate $(\frac{5}{6})^2$ as $\frac{5+2}{6+2} = \frac{7}{8}$ ! Exponents mean repeated multiplication, not addition. Always square both parts: $5^2 = 25$ and $6^2 = 36$ .

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 raise a fraction to a power, you're multiplying the entire fraction by itself. Since $(\frac{5}{6})^2 = \frac{5}{6} \times \frac{5}{6}$ , you multiply numerators together and denominators together!

Can I simplify the answer further?

Always check if your answer can be simplified! For $\frac{25}{36}$ , find the GCD of 25 and 36. Since 25 = 5² and 36 = 6², and they share no common factors, this fraction is already in simplest form.

What if the exponent was 3 instead of 2?

The same rule applies! $(\frac{5}{6})^3 = \frac{5^3}{6^3} = \frac{125}{216}$ . Just raise both the numerator and denominator to whatever power is given.

How is this different from adding fractions?

Completely different! Adding fractions requires a common denominator, but raising to a power just means multiplying the fraction by itself. No common denominators needed!

What's the fastest way to check my work?

Use multiplication! $\frac{5}{6} \times \frac{5}{6}$ should equal your answer. Multiply across: $\frac{5 \times 5}{6 \times 6} = \frac{25}{36}$ ✓

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime