Evaluate the Expression: Simplifying 1/4²

Negative Exponents with Fraction Conversion

Insert the corresponding expression:

142= \frac{1}{4^2}=

❤️ 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
00:00 Simplify the following problem
00:03 According to the laws of exponents, a number raised to the power of (-N)
00:06 is equal to the reciprocal number raised to the opposite power (-N)
00:09 We will apply this formula to our exercise
00:14 We'll convert to the reciprocal number and raise it to the opposite power (times(-1))
00:17 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Insert the corresponding expression:

142= \frac{1}{4^2}=

2

Step-by-step solution

To solve the problem of expressing 142\frac{1}{4^2} using powers with negative exponents:

  • Identify the base in the denominator: 4 raised to the power 2.
  • Apply the rule for negative exponents that states 1an=a−n\frac{1}{a^n} = a^{-n}.
  • Express 142\frac{1}{4^2} as 4−24^{-2}.

Thus, the expression 142\frac{1}{4^2} can be rewritten as 4−2 4^{-2} .

3

Final Answer

4−2 4^{-2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: 1an=a−n \frac{1}{a^n} = a^{-n} converts fractions to negative exponents
  • Technique: Move base from denominator to numerator, change exponent sign
  • Check: 4−2=142=116 4^{-2} = \frac{1}{4^2} = \frac{1}{16} matches original fraction ✓

Common Mistakes

Avoid these frequent errors
  • Adding negative sign to the base instead of exponent
    Don't write −42 -4^2 or −4−2 -4^{-2} = wrong base with wrong sign! The negative goes only on the exponent, not the base. Always keep the original base (4) and only change the exponent sign to get 4−2 4^{-2} .

Practice Quiz

Test your knowledge with interactive questions

\( 112^0=\text{?} \)

FAQ

Everything you need to know about this question

Why does the exponent become negative?

+

When you move a term from the denominator to the numerator (or vice versa), the exponent changes sign. This is the fundamental rule: 1an=a−n \frac{1}{a^n} = a^{-n} .

What's the difference between −42 -4^2 and 4−2 4^{-2} ?

+

−42=−(42)=−16 -4^2 = -(4^2) = -16 (negative of 4 squared), while 4−2=142=116 4^{-2} = \frac{1}{4^2} = \frac{1}{16} (positive fraction). The position of the negative sign matters!

Can I just flip the fraction instead?

+

Not quite! 142 \frac{1}{4^2} flipped would be 42 4^2 , but that's not equivalent. The negative exponent rule gives us the same value in a different form: 4−2 4^{-2} .

How do I remember this rule?

+

Think "flip and flip": when you flip a term from denominator to numerator, you also flip the sign of its exponent. Practice with simple examples like 123=2−3 \frac{1}{2^3} = 2^{-3} .

Does this work with any base and exponent?

+

Yes! The rule 1an=a−n \frac{1}{a^n} = a^{-n} works for any non-zero base a and any exponent n. Just remember to keep the base unchanged and only change the exponent sign.

🌟 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

Powers of a Fraction

Simplify the Expression: Converting 1/(20²) to Its Final Form
Click to solve
Calculate (8/221)^(-6): Negative Exponent Expression Solution
Click to solve

Negative Exponents