Calculate the Square of 4/5: Fraction Power Problem

Q: What if I accidentally calculated 4² ÷ 5² instead?

That would give you $ 16 ÷ 25 = 0.64 $, which is the decimal form of the same answer! $ \frac{16}{25} = 0.64 $, so you'd still be correct.

Q: How is this different from (4/5) × 2?

Be careful! $ \left(\frac{4}{5}\right)^2 $ means multiply by itself, while $ \frac{4}{5} \times 2 = \frac{8}{5} $ means multiply by 2. The exponent 2 means "squared," not "times 2"!

Q: Can I simplify 16/25 further?

No, $ \frac{16}{25} $ is already in simplest form! Since 16 and 25 share no common factors other than 1, this fraction cannot be reduced.

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

Then you'd calculate $ \left(\frac{4}{5}\right)^3 = \frac{4^3}{5^3} = \frac{64}{125} $. The same rule applies: raise both numerator and denominator to the given power.

Fraction Exponents with Square Powers

Insert the corresponding expression:

$\left(\frac{4}{5}\right)^2=$

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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)

00:08 equals the numerator and denominator, raised to the same power (N)

00:12 We will apply this formula to our exercise

00:16 We'll calculate each power and substitute accordingly

00:31 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:

$\left(\frac{4}{5}\right)^2=$

Step-by-step solution

To solve the problem of finding the value of $\left(\frac{4}{5}\right)^2$ , we will follow these steps:

Step 1: Identify the numerator and the denominator of the fraction. Here, the numerator is 4, and the denominator is 5.
Step 2: Apply the exponent to both the numerator and the denominator separately: $\left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2}$ .
Step 3: Calculate $\frac{4^2}{5^2}$ . This gives:
- The square of the numerator is $4^2 = 16$ .
- The square of the denominator is $5^2 = 25$ .
Thus, $\frac{4^2}{5^2} = \frac{16}{25}$ .

Since we successfully calculated $\left(\frac{4}{5}\right)^2 = \frac{16}{25}$ , this matches the choice labeled $\frac{16}{25}$ .

Therefore, the correct expression is $\frac{16}{25}$ .

Final Answer

$\frac{16}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Apply exponent to both numerator and denominator separately
Technique: $\left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2} = \frac{16}{25}$
Check: Verify numerator is 4² = 16 and denominator is 5² = 25 ✓

Common Mistakes

Avoid these frequent errors

Only squaring the numerator or denominator
Don't square just the numerator 4² = 16 and leave denominator as 5 = 16/5! This ignores the exponent rule for fractions and gives wrong results. Always apply the exponent to both the numerator and denominator: (4/5)² = 4²/5² = 16/25.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

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, the exponent applies to the entire fraction. This means both the numerator and denominator get raised to that power: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ .

What if I accidentally calculated 4² ÷ 5² instead?

That would give you $16 ÷ 25 = 0.64$ , which is the decimal form of the same answer! $\frac{16}{25} = 0.64$ , so you'd still be correct.

How is this different from (4/5) × 2?

Be careful! $\left(\frac{4}{5}\right)^2$ means multiply by itself, while $\frac{4}{5} \times 2 = \frac{8}{5}$ means multiply by 2. The exponent 2 means "squared," not "times 2"!

Can I simplify 16/25 further?

No, $\frac{16}{25}$ is already in simplest form! Since 16 and 25 share no common factors other than 1, this fraction cannot be reduced.

What if the exponent was 3 instead of 2?

Then you'd calculate $\left(\frac{4}{5}\right)^3 = \frac{4^3}{5^3} = \frac{64}{125}$ . The same rule applies: raise both numerator and denominator to the given power.

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