Calculate 7^(-24): Solving Negative Power Expressions

Q: Why isn't the answer negative when the exponent is negative?

Great question! The negative exponent doesn't make the result negative - it tells you to take the reciprocal. Think of it as flipping the fraction upside down, not changing the sign.

Q: How is this different from (-7)^24?

Very different! $ 7^{-24} = \frac{1}{7^{24}} $ (positive result), but $ (-7)^{24} = 7^{24} $ (positive because even exponent). The negative sign's location matters!

Q: Do I need to calculate the actual value of 7^24?

Usually not! Most problems want the answer in simplified form as $ \frac{1}{7^{24}} $. Computing $ 7^{24} $ gives an enormous number that's rarely needed.

Q: What if I see a^(-n/m) with a fractional negative exponent?

Same rule applies! $ a^{-\frac{n}{m}} = \frac{1}{a^{\frac{n}{m}}} $. Take the reciprocal and make the exponent positive - the fractional part stays the same.

Q: Is there a shortcut for remembering this rule?

Yes! Think "negative exponent = flip and positive". The base moves from numerator to denominator (or vice versa) and the exponent becomes positive. Easy to remember!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together!

00:08 When you raise any number, let's call it A, to the power of N,

00:13 it equals 1 divided by A to the power of negative N.

00:19 Let's use this rule on our question.

00:21 The number 7 becomes 1 divided by 7.

00:26 The exponent negative 24 becomes positive 24, because a negative times a negative is positive.

00:33 So our solution is: 1 over 7 to the power of 24.

00:38 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$7^{-24}=\text{?}$

2

Step-by-step solution

Using the rules of negative exponents: how to raise a number to a negative exponent:

$a^{-n}=\frac{1}{a^n}$ We apply it to the problem:

$7^{-24}=\frac{1}{7^{24}}$ Therefore, the correct answer is option D.

3

Final Answer

$\frac{1}{7^{24}}$

Key Points to Remember

Essential concepts to master this topic

Rule: Any number to a negative exponent equals one over that number to the positive exponent
Technique: $7^{-24} = \frac{1}{7^{24}}$ by flipping to reciprocal and making exponent positive
Check: Verify negative exponent gives reciprocal: $a^{-n} \cdot a^n = 1$ ✓

Common Mistakes

Avoid these frequent errors

Making the entire result negative
Don't think $7^{-24} = -\frac{1}{7^{24}}$ = negative fraction! The negative exponent only affects position (numerator vs denominator), not the sign of the result. Always remember: negative exponent means reciprocal, not negative value.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why isn't the answer negative when the exponent is negative?

+

Great question! The negative exponent doesn't make the result negative - it tells you to take the reciprocal. Think of it as flipping the fraction upside down, not changing the sign.

How is this different from (-7)^24?

+

Very different! $7^{-24} = \frac{1}{7^{24}}$ (positive result), but $(-7)^{24} = 7^{24}$ (positive because even exponent). The negative sign's location matters!

Do I need to calculate the actual value of 7^24?

+

Usually not! Most problems want the answer in simplified form as $\frac{1}{7^{24}}$ . Computing $7^{24}$ gives an enormous number that's rarely needed.

What if I see a^(-n/m) with a fractional negative exponent?

+

Same rule applies! $a^{-\frac{n}{m}} = \frac{1}{a^{\frac{n}{m}}}$ . Take the reciprocal and make the exponent positive - the fractional part stays the same.

Is there a shortcut for remembering this rule?

+

Yes! Think "negative exponent = flip and positive". The base moves from numerator to denominator (or vice versa) and the exponent becomes positive. Easy to remember!

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Calculate 7^(-24): Solving Negative Power Expressions

Negative Exponents with Large Integer Powers

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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 isn't the answer negative when the exponent is negative?

How is this different from (-7)^24?

Do I need to calculate the actual value of 7^24?

What if I see a^(-n/m) with a fractional negative exponent?

Is there a shortcut for remembering this rule?

🌟 Unlock Your Math Potential

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