Simplify the Expression: Converting 1/(20²) to Its Final Form

Q: Why does the exponent become negative when I move it?

Think of it as "paying a penalty" for moving from the denominator to the numerator. The negative exponent tells you the number is really in the denominator: $ 20^{-2} $ means "20 squared, but in the bottom of a fraction."

Q: Is $ 20^{-2} $ the same as $ -20^2 $ ?

No! $ 20^{-2} = \frac{1}{400} $ (positive), but $ -20^2 = -400 $ (negative). The negative sign's position matters: negative exponent vs negative base.

Q: Can I calculate the decimal value instead?

You could calculate $ \frac{1}{20^2} = \frac{1}{400} = 0.0025 $, but the question asks for the equivalent expression, not the decimal value. Stick with $ 20^{-2} $.

Q: What if the base was negative, like $ \frac{1}{(-5)^3} $ ?

Same rule applies! $ \frac{1}{(-5)^3} = (-5)^{-3} $. The parentheses stay with the base, and only the exponent becomes negative. Keep the entire base the same.

Q: How do I remember this rule?

Think: "Flip the fraction, flip the sign" - when you move a power from bottom to top (or vice versa), the exponent sign flips too. It's like the exponent's way of remembering where it came from!

Negative Exponents with Reciprocal Conversion

Insert the corresponding expression:

$\frac{1}{20^2}=$

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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 exponent laws, a number raised to the power of (-N)

00:06 equals the reciprocal number raised to the opposite power (N)

00:10 We'll apply this formula to our exercise

00:13 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

Understand the problem

Insert the corresponding expression:

$\frac{1}{20^2}=$

Step-by-step solution

To solve this problem, we will use the properties of exponents. Specifically, we will convert the expression $\frac{1}{20^2}$ into a form that uses a negative exponent. The general relationship is that $\frac{1}{a^n} = a^{-n}$ .

Applying this rule to the given expression:

Step 1: Identify the current form, which is $\frac{1}{20^2}$ .
Step 2: Apply the negative exponent rule: $\frac{1}{20^2} = 20^{-2}$ .
Step 3: This expression, $20^{-2}$ , represents $\frac{1}{20^2}$ using a negative exponent.

Therefore, the expression $\frac{1}{20^2}$ can be expressed as $20^{-2}$ , which aligns with choice 1.

Final Answer

$20^{-2}$

Key Points to Remember

Essential concepts to master this topic

Rule: $\frac{1}{a^n} = a^{-n}$ converts fractions to negative exponents
Technique: Move base from denominator to numerator and flip exponent sign
Check: Verify $20^{-2} = \frac{1}{20^2} = \frac{1}{400}$ ✓

Common Mistakes

Avoid these frequent errors

Adding negative signs incorrectly
Don't write $-20^{-2}$ when converting $\frac{1}{20^2}$ = negative answer when original is positive! The negative sign applies to the exponent only, not the base. Always keep the base positive and make only the exponent negative.

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 I move it?

Think of it as "paying a penalty" for moving from the denominator to the numerator. The negative exponent tells you the number is really in the denominator: $20^{-2}$ means "20 squared, but in the bottom of a fraction."

Is $20^{-2}$ the same as $-20^2$ ?

No! $20^{-2} = \frac{1}{400}$ (positive), but $-20^2 = -400$ (negative). The negative sign's position matters: negative exponent vs negative base.

Can I calculate the decimal value instead?

You could calculate $\frac{1}{20^2} = \frac{1}{400} = 0.0025$ , but the question asks for the equivalent expression, not the decimal value. Stick with $20^{-2}$ .

What if the base was negative, like $\frac{1}{(-5)^3}$ ?

Same rule applies! $\frac{1}{(-5)^3} = (-5)^{-3}$ . The parentheses stay with the base, and only the exponent becomes negative. Keep the entire base the same.

How do I remember this rule?

Think: "Flip the fraction, flip the sign" - when you move a power from bottom to top (or vice versa), the exponent sign flips too. It's like the exponent's way of remembering where it came from!

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Simplify the Expression: Converting 1/(20²) to Its Final Form

Negative Exponents with Reciprocal Conversion

❤️ 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 the exponent become negative when I move it?

Is $20^{-2}$ the same as $-20^2$ ?

Can I calculate the decimal value instead?

What if the base was negative, like $\frac{1}{(-5)^3}$ ?

How do I remember this rule?

🌟 Unlock Your Math Potential

More Questions

Powers of a Fraction

Calculate (8/221)^(-6): Negative Exponent Expression Solution

Evaluate (1×5)/(4×6) Raised to Negative 2nd Power

Evaluate the Expression: Simplifying 1/4²

Convert the Expression: Finding the Value of 1/3²

Negative Exponents

Convert the Expression: Writing 1/5² in Standard Form

Express 1/6^7: Converting a Fraction to Negative Exponent Form

Simplify the Expression: Converting 1/(20²) to Its Final Form

Negative Exponents with Reciprocal Conversion

❤️ 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 the exponent become negative when I move it?

Is 20−2 20^{-2} 20−2 the same as −202 -20^2 −202?

Can I calculate the decimal value instead?

What if the base was negative, like 1(−5)3 \frac{1}{(-5)^3} (−5)31​?

How do I remember this rule?

🌟 Unlock Your Math Potential

More Questions

Powers of a Fraction

Calculate (8/221)^(-6): Negative Exponent Expression Solution

Evaluate (1×5)/(4×6) Raised to Negative 2nd Power

Evaluate the Expression: Simplifying 1/4²

Convert the Expression: Finding the Value of 1/3²

Negative Exponents

Convert the Expression: Writing 1/5² in Standard Form

Express 1/6^7: Converting a Fraction to Negative Exponent Form

Is $20^{-2}$ the same as $-20^2$ ?

What if the base was negative, like $\frac{1}{(-5)^3}$ ?