Solve for 4^(-1): Converting Negative Exponent to Reciprocal

Negative Exponents with Single Base Numbers

4−1=? 4^{-1}=\text{?}

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's solve this problem together.
00:06 Remember, if we have a number, A, raised to the power of negative N.
00:11 And it's not zero, then we can write it as, one divided by A to the power of N.
00:17 Let's see how this applies to our question.
00:21 For example, four to the power of negative one becomes one over four.
00:26 The power negative one, turns into a positive one in the denominator.
00:31 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

4−1=? 4^{-1}=\text{?}

2

Step-by-step solution

We begin by using the power rule of negative exponents.

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

4−1=141=14 4^{-1}=\frac{1}{4^1}=\frac{1}{4} We can therefore deduce that the correct answer is option B.

3

Final Answer

14 \frac{1}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Any negative exponent equals one over positive exponent
  • Technique: 4−1=141=14 4^{-1} = \frac{1}{4^1} = \frac{1}{4}
  • Check: Multiply answer by original base: 14×4=1 \frac{1}{4} \times 4 = 1 ✓

Common Mistakes

Avoid these frequent errors
  • Making the answer negative when seeing negative exponent
    Don't think 4^(-1) = -1/4 just because you see a negative sign! The negative exponent only affects position (top/bottom of fraction), not the sign of the result. Always remember: negative exponents create reciprocals, not negative numbers.

Practice Quiz

Test your knowledge with interactive questions

\( (2^3)^6 = \)

FAQ

Everything you need to know about this question

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

+

Great question! The negative exponent tells you to flip the fraction, not make the answer negative. Think of it as: negative exponent = reciprocal, not negative number.

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

+

4−1=14 4^{-1} = \frac{1}{4} (positive fraction), but −41=−4 -4^1 = -4 (negative whole number). The position of the negative sign matters!

How do I remember the negative exponent rule?

+

Think "flip and drop"! Flip the base to the bottom of a fraction, then drop the negative from the exponent. So a−n a^{-n} becomes 1an \frac{1}{a^n} .

Can I check my answer somehow?

+

Yes! Multiply your answer by the original base. If you get 1, you're correct! For example: 14×4=1 \frac{1}{4} \times 4 = 1 ✓

What if the base was a fraction instead?

+

If you had (14)−1 \left(\frac{1}{4}\right)^{-1} , you'd flip the fraction to get 41=4 \frac{4}{1} = 4 . Negative exponents always create reciprocals!

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations

Negative Exponents

Calculate 2^(-5): Solving Negative Exponent Expression
Click to solve
Solve (-7)^(-3): Calculating Negative Number with Negative Exponent
Click to solve

Exponents Rules

Simplify x^-a: Understanding Negative Exponent Notation
Click to solve
Calculate 7^(-24): Solving Negative Power Expressions
Click to solve

Applying Combined Exponents Rules

Solve 19^-2: Calculating a Specific Negative Exponent
Click to solve
Evaluate the Expression: Finding the Value of 8^(-2x)
Click to solve