Simplify the Complex Fraction: 1/(X^7/X^6) Step by Step

Question

$\frac{1}{\frac{X^7}{X^6}}=$

00:08 Let's solve this problem together.

00:12 We'll use the formula for dividing powers with the same base.

00:16 When dividing, we keep the base and subtract the exponents.

00:20 Now, let's apply this to our exercise step by step.

00:26 We subtract the exponent in the denominator from the exponent in the numerator.

00:40 Remember, a negative exponent means we flip it between top and bottom.

00:48 Now, let's use this rule in our example.

00:55 And there you have it, the solution!

First, we will focus on the exercise with a fraction in the denominator. We will solve it using the formula:

$\frac{a^n}{a^m}= a^{n-m}$

$\frac{x^7}{x^6}=x^{7-6}=x^1$

Therefore, we get:

$\frac{1}{x}$

We know that a product raised to the 0 is equal to 1 and therefore:

$\frac{x^0}{x^1}=x^{(0-1)}=x^{-1}$

$X^{-1}$