Evaluate (3/8)^(-5): Negative Exponents with Fractions

Q: Why does a negative exponent flip the fraction?

A negative exponent means "take the reciprocal." So $ \left(\frac{3}{8}\right)^{-5} $ becomes $ \frac{1}{\left(\frac{3}{8}\right)^5} $, which simplifies to $ \left(\frac{8}{3}\right)^5 $!

Q: Does the negative exponent make my answer negative?

No! The negative exponent only affects the position of the fraction (flips it), not the sign of your final answer. Your result stays positive unless there's a separate negative sign.

Q: What's the difference between $ \left(\frac{3}{8}\right)^{-5} $ and $ -\left(\frac{3}{8}\right)^5 $ ?

The first has a negative exponent which flips the fraction. The second has a negative sign in front, making the whole result negative. They're completely different operations!

Q: Can I work with the numerator and denominator separately?

Not with negative exponents! You must treat $ \left(\frac{3}{8}\right)^{-5} $ as one unit and flip the entire fraction first, then apply the positive exponent.

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

Think: "Negative exponent = reciprocal" So the top becomes bottom, and bottom becomes top. $ \frac{3}{8} $ flips to $ \frac{8}{3} $!

Negative Exponents with Fraction Inversion

Insert the corresponding expression:

$\left(\frac{3}{8}\right)^{-5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's simplify this problem together.

00:11 Remember, when a fraction is raised to a negative power, it's the same as raising its reciprocal to a positive power.

00:18 We'll use this rule to solve our exercise.

00:21 First, let's flip the fraction.

00:24 Then, we'll raise it to the positive power instead.

00:27 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:

$\left(\frac{3}{8}\right)^{-5}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given fraction and the negative exponent.
Step 2: Apply the conversion rule from negative to positive exponents on fractions.

Now, let's work through each step:
Step 1: The given expression is $\left(\frac{3}{8}\right)^{-5}$ . This indicates a fraction raised to a negative power.
Step 2: Applying the rule $(\frac{a}{b})^{-n} = (\frac{b}{a})^{n}$ , we invert the fraction and change the exponent to positive. This gives us the expression $\left(\frac{8}{3}\right)^5$ .

Therefore, the solution to the problem is $\left(\frac{8}{3}\right)^5$ .

Final Answer

$\left(\frac{8}{3}\right)^5$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative exponent means flip fraction and make positive
Technique: $\left(\frac{3}{8}\right)^{-5} = \left(\frac{8}{3}\right)^5$ by inverting base
Check: Verify the base is flipped and exponent becomes positive ✓

Common Mistakes

Avoid these frequent errors

Adding negative sign to the result
Don't write $-\left(\frac{8}{3}\right)^5$ = negative answer! A negative exponent doesn't make the result negative, it just means "take the reciprocal." Always flip the fraction but keep the result positive.

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." So $\left(\frac{3}{8}\right)^{-5}$ becomes $\frac{1}{\left(\frac{3}{8}\right)^5}$ , which simplifies to $\left(\frac{8}{3}\right)^5$ !

Does the negative exponent make my answer negative?

No! The negative exponent only affects the position of the fraction (flips it), not the sign of your final answer. Your result stays positive unless there's a separate negative sign.

What's the difference between $\left(\frac{3}{8}\right)^{-5}$ and $-\left(\frac{3}{8}\right)^5$ ?

The first has a negative exponent which flips the fraction. The second has a negative sign in front, making the whole result negative. They're completely different operations!

Can I work with the numerator and denominator separately?

Not with negative exponents! You must treat $\left(\frac{3}{8}\right)^{-5}$ as one unit and flip the entire fraction first, then apply the positive exponent.

How do I remember which way to flip the fraction?

Think: "Negative exponent = reciprocal" So the top becomes bottom, and bottom becomes top. $\frac{3}{8}$ flips to $\frac{8}{3}$ !

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Evaluate (3/8)^(-5): Negative Exponents with Fractions

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 answer negative?

What's the difference between $\left(\frac{3}{8}\right)^{-5}$ and $-\left(\frac{3}{8}\right)^5$ ?

Can I work with the numerator and denominator separately?

How do I remember which way to flip the fraction?

🌟 Unlock Your Math Potential

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Evaluate (3/8)^(-5): Negative Exponents with Fractions

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 answer negative?

What's the difference between (38)−5 \left(\frac{3}{8}\right)^{-5} (83​)−5 and −(38)5 -\left(\frac{3}{8}\right)^5 −(83​)5?

Can I work with the numerator and denominator separately?

How do I remember which way to flip the fraction?

🌟 Unlock Your Math Potential

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What's the difference between $\left(\frac{3}{8}\right)^{-5}$ and $-\left(\frac{3}{8}\right)^5$ ?