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

Question

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

00:00 Solve

00:03 We'll use the formula for dividing powers with the same base

00:07 We'll get the base with an exponent that is the difference of the exponents

00:11 We'll use this formula in our exercise

00:18 We'll subtract between the powers

00:32 A negative exponent switches between numerator and denominator

00:40 We'll use this formula in our exercise

00:47 And this is the solution to the question

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:

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

$X^{-1}$