Simplify (a/b)^9: Evaluating the Ninth Power of a Fraction

Insert the corresponding expression:

(ab)9= \left(\frac{a}{b}\right)^9=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's simplify the following problem.
00:10 Remember, when a fraction is raised to a power, like N,
00:14 both the numerator and denominator are raised to that power, N.
00:19 Now, let's apply this rule to our exercise.
00:23 And that's how we find the solution!

Step-by-step written solution

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1

Understand the problem

Insert the corresponding expression:

(ab)9= \left(\frac{a}{b}\right)^9=

2

Step-by-step solution

The problem asks us to express (ab)9\left(\frac{a}{b}\right)^9 using exponent rules. We will use the rule for the power of a fraction, which states:

(ab)n=anbn\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}

Applying this rule, we get:

(ab)9=a9b9\left(\frac{a}{b}\right)^9 = \frac{a^9}{b^9}

This method ensures that the exponent 99 is applied to both the numerator and the denominator of the fraction.

Therefore, the solution to the problem is a9b9\frac{a^9}{b^9}.

3

Final Answer

a9b9 \frac{a^9}{b^9}

Practice Quiz

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\( 112^0=\text{?} \)

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