Solve (1/60) Raised to Negative Fourth Power: Fraction Exponent Challenge

Q: Why doesn't the negative exponent make the answer negative?

Great question! A negative exponent doesn't make the result negative - it tells you to flip the fraction. Think of it as: $ a^{-n} = \frac{1}{a^n} $. The negative sign is about position, not sign!

Q: How do I flip a fraction that's already 1/something?

When you have $ \frac{1}{60} $ and need to flip it, you get $ \frac{60}{1} $, which simply equals 60. So $ \left(\frac{1}{60}\right)^{-4} $ becomes $ 60^4 $!

Q: What if the fraction had a different numerator, like 3/60?

Same rule applies! $ \left(\frac{3}{60}\right)^{-4} = \left(\frac{60}{3}\right)^{4} = 20^4 $. Always flip the entire fraction, then apply the positive exponent.

Q: Do I need to calculate 60^4 to get the final answer?

Not usually! Most problems ask for the simplified expression, which is $ 60^4 $. Only calculate the actual number (12,960,000) if specifically asked.

Q: What's the difference between 60^-4 and (1/60)^-4?

$ 60^{-4} = \frac{1}{60^4} $ while $ \left(\frac{1}{60}\right)^{-4} = 60^4 $. They're reciprocals of each other! The parentheses make a huge difference in the order of operations.

Negative Exponents with Fractional Bases

Insert the corresponding expression:

$\left(\frac{1}{60}\right)^{-4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's make this problem easier to understand.

00:12 When a fraction is raised to the power of negative N,

00:16 it's the same as the reciprocal of the fraction raised to the power of N.

00:21 Now, we'll use this rule to solve our problem.

00:25 First, we flip the fraction around.

00:29 Then, we raise it to the positive power of N.

00:34 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\left(\frac{1}{60}\right)^{-4}=$

Step-by-step solution

To solve for $\left(\frac{1}{60}\right)^{-4}$ , we apply the rule for negative exponents.

Step 1: Use the negative exponent rule: For any non-zero number $a$ , $a^{-n} = \frac{1}{a^n}$ . Thus,

$\left(\frac{1}{60}\right)^{-4} = \left(\frac{60}{1}\right)^4$ .

Step 2: Simplify $\left(\frac{60}{1}\right)^4$ by recognizing the identity $\frac{60}{1} = 60$ , so it follows that:

$\left(\frac{60}{1}\right)^4 = 60^4$ .

Therefore, the simplified expression is $60^4$ .

The correct answer is $60^4$

Final Answer

$60^4$

Key Points to Remember

Essential concepts to master this topic

Rule: For negative exponents, flip the base and make exponent positive
Technique: $\left(\frac{1}{60}\right)^{-4} = \left(\frac{60}{1}\right)^{4} = 60^4$
Check: Negative exponent creates reciprocal: $\frac{1}{60^4}$ flipped gives $60^4$ ✓

Common Mistakes

Avoid these frequent errors

Adding negative sign to final answer
Don't write -60^4 thinking negative exponent means negative answer! The negative exponent only tells you to flip the fraction, not make the result negative. Always remember: negative exponents create reciprocals, not negative numbers.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why doesn't the negative exponent make the answer negative?

Great question! A negative exponent doesn't make the result negative - it tells you to flip the fraction. Think of it as: $a^{-n} = \frac{1}{a^n}$ . The negative sign is about position, not sign!

How do I flip a fraction that's already 1/something?

When you have $\frac{1}{60}$ and need to flip it, you get $\frac{60}{1}$ , which simply equals 60. So $\left(\frac{1}{60}\right)^{-4}$ becomes $60^4$ !

What if the fraction had a different numerator, like 3/60?

Same rule applies! $\left(\frac{3}{60}\right)^{-4} = \left(\frac{60}{3}\right)^{4} = 20^4$ . Always flip the entire fraction, then apply the positive exponent.

Do I need to calculate 60^4 to get the final answer?

Not usually! Most problems ask for the simplified expression, which is $60^4$ . Only calculate the actual number (12,960,000) if specifically asked.

What's the difference between 60^-4 and (1/60)^-4?

$60^{-4} = \frac{1}{60^4}$ while $\left(\frac{1}{60}\right)^{-4} = 60^4$ . They're reciprocals of each other! The parentheses make a huge difference in the order of operations.

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Solve (1/60) Raised to Negative Fourth Power: Fraction Exponent Challenge

Negative Exponents with Fractional Bases

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why doesn't the negative exponent make the answer negative?

How do I flip a fraction that's already 1/something?

What if the fraction had a different numerator, like 3/60?

Do I need to calculate 60^4 to get the final answer?

What's the difference between 60^-4 and (1/60)^-4?

🌟 Unlock Your Math Potential

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