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

Q: Why does a negative exponent flip the fraction?

A negative exponent means "take the reciprocal." Since $ a^{-n} = \frac{1}{a^n} $, when you have $ \left(\frac{10}{13}\right)^{-2} $, you get $ \frac{1}{\left(\frac{10}{13}\right)^2} = \left(\frac{13}{10}\right)^2 $!

Q: Does the negative exponent make my final answer negative?

No! The negative exponent only tells you to flip the fraction. The final answer $ \left(\frac{13}{10}\right)^2 $ is still positive because you're squaring a positive number.

Q: What if I had a positive number instead of a fraction?

Same rule applies! For example, $ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} $. The negative exponent always means "take the reciprocal."

Q: How do I remember which way to flip the fraction?

Think of it as "opposite day" - whatever was on top goes to the bottom, and vice versa. The 10 and 13 just switch places!

Q: What happens after I flip the fraction?

Once you flip it, treat the exponent as positive! So $ \left(\frac{13}{10}\right)^2 $ means you square both the numerator and denominator normally.

Negative Exponents with Fraction Inversion

Insert the corresponding expression:

$\left(\frac{10}{13}\right)^{-2}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the following problem

00:04 According to the laws of exponents, any fraction raised to the negative exponent (-N)

00:08 equals the reciprocal fraction with the same exponent (N) multiplied by (-1)

00:15 We will apply this formula to our exercise

00:22 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:

$\left(\frac{10}{13}\right)^{-2}=$

Step-by-step solution

To solve the problem, apply the negative exponent rule:

For any fraction $\frac{a}{b}$ with a negative exponent $-n$ , apply the rule: $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^{n}$ .

Apply this rule to the given expression $\left(\frac{10}{13}\right)^{-2}$ :

$\left(\frac{10}{13}\right)^{-2} = \left(\frac{13}{10}\right)^{2}$

Therefore, the correct expression with a positive exponent is $\left(\frac{13}{10}\right)^{2}$ .

In the provided choices, this is option:

$\left(\frac{13}{10}\right)^2$

Hence, the correct expression is $\left(\frac{13}{10}\right)^2$ .

Final Answer

$\left(\frac{13}{10}\right)^2$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative exponents flip fractions and make exponents positive
Technique: $\left(\frac{10}{13}\right)^{-2} = \left(\frac{13}{10}\right)^{2}$
Check: Original fraction flipped with positive exponent only ✓

Common Mistakes

Avoid these frequent errors

Applying negative sign to the fraction
Don't make $\left(\frac{10}{13}\right)^{-2} = -\left(\frac{13}{10}\right)^2$ ! The negative exponent doesn't make the answer negative - it flips the fraction. Always flip the numerator and denominator, then apply the positive exponent.

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 flip the fraction?

A negative exponent means "take the reciprocal." Since $a^{-n} = \frac{1}{a^n}$ , when you have $\left(\frac{10}{13}\right)^{-2}$ , you get $\frac{1}{\left(\frac{10}{13}\right)^2} = \left(\frac{13}{10}\right)^2$ !

Does the negative exponent make my final answer negative?

No! The negative exponent only tells you to flip the fraction. The final answer $\left(\frac{13}{10}\right)^2$ is still positive because you're squaring a positive number.

What if I had a positive number instead of a fraction?

Same rule applies! For example, $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$ . The negative exponent always means "take the reciprocal."

How do I remember which way to flip the fraction?

Think of it as "opposite day" - whatever was on top goes to the bottom, and vice versa. The 10 and 13 just switch places!

What happens after I flip the fraction?

Once you flip it, treat the exponent as positive! So $\left(\frac{13}{10}\right)^2$ means you square both the numerator and denominator normally.

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

Negative Exponents with Fraction Inversion

❤️ 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 flip the fraction?

Does the negative exponent make my final answer negative?

What if I had a positive number instead of a fraction?

How do I remember which way to flip the fraction?

What happens after I flip the fraction?

🌟 Unlock Your Math Potential

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