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

Question

Insert the corresponding expression:

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

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!

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

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

Applying this rule, we get:

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

This method ensures that the exponent $9$ is applied to both the numerator and the denominator of the fraction.

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

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