Simplify 5^-2: Negative Exponent Calculation Step-by-Step

Q: Why does a negative exponent make the answer smaller?

A negative exponent means "how many times do I divide by this number?" So $ 5^{-2} $ means divide by 5 twice, which gives us $ \frac{1}{5 \times 5} = \frac{1}{25} $.

Q: Is there a difference between 5^(-2) and -5^2?

Yes, huge difference! $ 5^{-2} = \frac{1}{25} $ (positive), while $ -5^2 = -25 $ (negative). The negative sign's position completely changes the meaning!

Q: Can I just move the decimal point instead?

No! Moving decimal points only works for powers of 10. For other bases like 5, you must use the rule $ a^{-n} = \frac{1}{a^n} $ and calculate the denominator.

Q: What if the base is already a fraction?

Great question! If you have $ (\frac{2}{3})^{-2} $, flip the entire fraction: $ (\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{9}{4} $.

Q: How do I remember this rule?

Think "negative means flip!" The negative exponent tells you to flip the base from numerator to denominator (or vice versa), then use the positive exponent.

Negative Exponents with Power Rule

$5^{-2}$

❤️ 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 Simply

00:09 Any number to the power of 1 is always equal to itself

00:20 We'll use the formula for negative powers

00:23 When we have a negative power (-M) on any fraction (A/B)

00:27 We get the reciprocal number (B/A) raised to the positive exponent (M)

00:35 We'll use this formula in our exercise

00:39 We'll substitute the reciprocal number and the opposite power

00:44 Now we'll use the formula for powers of fractions

00:50 We'll make sure to raise both numerator and denominator to the appropriate power

00:55 We'll use this formula in our exercise

00:58 We'll make sure to raise both numerator and denominator to the power, and calculate

01:03 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5^{-2}$

Step-by-step solution

We use the property of powers of a negative exponent:

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

$5^{-2}=\frac{1}{5^2}=\frac{1}{25}$

Therefore, the correct answer is option d.

Final Answer

$\frac{1}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative exponents flip the base to denominator: $a^{-n} = \frac{1}{a^n}$
Technique: Apply positive exponent first: $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$
Check: Multiply result by original base squared: $\frac{1}{25} \times 25 = 1$ ✓

Common Mistakes

Avoid these frequent errors

Making the exponent negative in numerator
Don't write 5^(-2) as -25 or negative fractions! This confuses the negative sign with the exponent rule. Always flip the base to the denominator and make the exponent positive: $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$ .

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why does a negative exponent make the answer smaller?

A negative exponent means "how many times do I divide by this number?" So $5^{-2}$ means divide by 5 twice, which gives us $\frac{1}{5 \times 5} = \frac{1}{25}$ .

Is there a difference between 5^(-2) and -5^2?

Yes, huge difference! $5^{-2} = \frac{1}{25}$ (positive), while $-5^2 = -25$ (negative). The negative sign's position completely changes the meaning!

Can I just move the decimal point instead?

No! Moving decimal points only works for powers of 10. For other bases like 5, you must use the rule $a^{-n} = \frac{1}{a^n}$ and calculate the denominator.

What if the base is already a fraction?

Great question! If you have $(\frac{2}{3})^{-2}$ , flip the entire fraction: $(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{9}{4}$ .

How do I remember this rule?

Think "negative means flip!" The negative exponent tells you to flip the base from numerator to denominator (or vice versa), then use the positive exponent.

🌟 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

Simplify 5^-2: Negative Exponent Calculation Step-by-Step

Negative Exponents with Power Rule

❤️ 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 does a negative exponent make the answer smaller?

Is there a difference between 5^(-2) and -5^2?

Can I just move the decimal point instead?

What if the base is already a fraction?

How do I remember this rule?

🌟 Unlock Your Math Potential

More Questions

Applying Combined Exponents Rules

Simplify the Expression: 2^(2x+1) · 2^5 · 2^(3x)

Simplify the Complex Fraction: 1/(X^7/X^6) Step by Step

Evaluate (1/4)^(-1): Converting Negative Exponents to Reciprocals

Calculate (2/6)³: Cube of a Simple Fraction

Exponents Rules

Solve: [(1/7)^-1]^4 Using Laws of Negative Exponents

Simplify: 4^(2y) × 4^(-5) × 4^(-y) × 4^6 Using Laws of Exponents

Solve (4²/7⁴)²: Calculating Powers of Complex Fractions

Evaluate 5⁰: Understanding the Zero Exponent Rule

Negative Exponents

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

Calculate 2^(-5): Solving Negative Exponent Expression