Calculate (1/20)^(-7): Negative Exponent Expression Evaluation

Q: Why doesn't the negative exponent make the answer negative?

The negative sign in the exponent is an instruction to take the reciprocal, not to make the result negative. Think of it as "flip and make positive" rather than adding a negative sign!

Q: How do I remember the rule for $ \left(\frac{1}{a}\right)^{-n} $ ?

Remember: "Flip twice, get back home!" The fraction $ \frac{1}{20} $ is already flipped from 20, so the negative exponent flips it back to $ 20^7 $.

Q: What's the difference between $ 20^{-7} $ and $ 20^7 $ ?

$ 20^{-7} = \frac{1}{20^7} $ (a very small number), while $ 20^7 $ is a very large number. The negative exponent creates the reciprocal!

Q: Can I solve this step by step instead of using the rule?

Yes! You can write: $ \left(\frac{1}{20}\right)^{-7} = \frac{1}{\left(\frac{1}{20}\right)^7} = \frac{1}{\frac{1}{20^7}} = 20^7 $. Both methods give the same answer!

Q: Does this rule work for any fraction with negative exponents?

Absolutely! For any fraction $ \left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n $. Just flip the fraction and make the exponent positive!

Negative Exponents with Fractional Bases

Insert the corresponding expression:

$\left(\frac{1}{20}\right)^{-7}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's simplify this problem.

00:11 When a fraction is raised to a power like N,

00:15 both the top and bottom are raised to that same power, N.

00:20 Let's use this rule in our exercise now.

00:26 Remember, one raised to any power is always one.

00:34 For any number raised to a power, N,

00:37 it equals the reciprocal to power N, times negative one.

00:43 Let's apply this in our example now.

00:46 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\left(\frac{1}{20}\right)^{-7}=$

Step-by-step solution

To simplify the expression $\left(\frac{1}{20}\right)^{-7}$ , we will apply the rule for negative exponents. The key idea is that a negative exponent indicates taking the reciprocal and converting the exponent to a positive:

Start with the expression: $\left(\frac{1}{20}\right)^{-7}$ .
Apply the negative exponent rule: $\left(\frac{1}{a}\right)^{-n} = a^n$ .
For our expression: $\left(\frac{1}{20}\right)^{-7}$ becomes $20^7$ .

Therefore, $\left(\frac{1}{20}\right)^{-7}$ simplifies to $20^7$ .

Thus, the correct answer is $20^7$ .

Final Answer

$20^7$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative exponent means flip and make positive
Technique: $\left(\frac{1}{20}\right)^{-7} = 20^7$ by reciprocal rule
Check: Verify by converting back: $20^7 = \frac{1}{\left(\frac{1}{20}\right)^7}$ ✓

Common Mistakes

Avoid these frequent errors

Applying negative sign to the entire expression
Don't think $\left(\frac{1}{20}\right)^{-7} = -20^7$ ! The negative exponent doesn't make the answer negative - it indicates reciprocal operation. Always remember: negative exponent means flip the base, not make it negative.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why doesn't the negative exponent make the answer negative?

The negative sign in the exponent is an instruction to take the reciprocal, not to make the result negative. Think of it as "flip and make positive" rather than adding a negative sign!

How do I remember the rule for $\left(\frac{1}{a}\right)^{-n}$ ?

Remember: "Flip twice, get back home!" The fraction $\frac{1}{20}$ is already flipped from 20, so the negative exponent flips it back to $20^7$ .

What's the difference between $20^{-7}$ and $20^7$ ?

$20^{-7} = \frac{1}{20^7}$ (a very small number), while $20^7$ is a very large number. The negative exponent creates the reciprocal!

Can I solve this step by step instead of using the rule?

Yes! You can write: $\left(\frac{1}{20}\right)^{-7} = \frac{1}{\left(\frac{1}{20}\right)^7} = \frac{1}{\frac{1}{20^7}} = 20^7$ . Both methods give the same answer!

Does this rule work for any fraction with negative exponents?

Absolutely! For any fraction $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$ . Just flip the fraction and make the exponent positive!

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Calculate (1/20)^(-7): Negative Exponent Expression Evaluation

Negative Exponents with Fractional Bases

❤️ 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 doesn't the negative exponent make the answer negative?

How do I remember the rule for $\left(\frac{1}{a}\right)^{-n}$ ?

What's the difference between $20^{-7}$ and $20^7$ ?

Can I solve this step by step instead of using the rule?

Does this rule work for any fraction with negative exponents?

🌟 Unlock Your Math Potential

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Calculate (1/20)^(-7): Negative Exponent Expression Evaluation

Negative Exponents with Fractional Bases

❤️ 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 doesn't the negative exponent make the answer negative?

How do I remember the rule for (1a)−n \left(\frac{1}{a}\right)^{-n} (a1​)−n?

What's the difference between 20−7 20^{-7} 20−7 and 207 20^7 207?

Can I solve this step by step instead of using the rule?

Does this rule work for any fraction with negative exponents?

🌟 Unlock Your Math Potential

More Questions

Powers of a Fraction

Solve (5/7)^-7: Converting Negative Exponent to Positive

Solve (10/13) Raised to Negative 2 Power: Fraction Exponent Practice

Evaluate (3/7)^(-4): Negative Exponent Expression

Evaluate (2/5)^(-3): Negative Exponents with Fractions

Negative Exponents

Evaluate (15/21) Raised to the Negative Third Power: Step-by-Step Solution

Solve (1/60) Raised to Negative Fourth Power: Fraction Exponent Challenge

Examine the Power of Inversion: Simplify 300^-4 x (1/300)^-4

Simplify This Complex Expression: (13/2)^0 ⋅ (2/13)^(-2) ⋅ (13/2)^(-5)

How do I remember the rule for $\left(\frac{1}{a}\right)^{-n}$ ?

What's the difference between $20^{-7}$ and $20^7$ ?