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Exercises Polynomials and factoring

Example 10.45 from Prealgebra, 10.4 Divide Monomials

Divide Monomials: example 10.45

Simplify:

ⓐ $\frac{x^{10}}{x^{8}}$
ⓑ $\frac{2^{9}}{2^{2}}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.

ⓐ

Since 10 > 8, there are more factors of $x$ in the numerator. $\frac{x^{10}}{x^{8}}$

Use the quotient property with $m > n, \frac{a^{m}}{a^{n}} = a^{m - n}$ .

Simplify. $x^{2}$

ⓑ

Since 9 > 2, there are more factors of 2 in the numerator. $\frac{2^{9}}{2^{2}}$

Use the quotient property with $m > n, \frac{a^{m}}{a^{n}} = a^{m - n} .$

Simplify. $2^{7}$

Notice that when the larger exponent is in the numerator, we are left with factors in the numerator.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify:

ⓐ $\frac{x^{12}}{x^{9}}$
ⓑ $\frac{7^{14}}{7^{5}}$

How did it go?

PreviousMultiply Polynomials: example 10.44 Next Divide Monomials: example 10.46

From Prealgebra (1st edition) by OpenStax (Rice University), section 10.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.