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Exercises Polynomials and factoring

Example 6.70 from Elementary Algebra, 6.5 Divide Monomials

Divide Monomials: example 6.70

Simplify: $\frac{{(x^{3})}^{4} {(x^{2})}^{5}}{{(x^{6})}^{5}} .$

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

$\frac{{(x^{3})}^{4} {(x^{2})}^{5}}{{(x^{6})}^{5}}$

Use the Power Property, ${(a^{m})}^{n} = a^{m \cdot n}$ . $\frac{(x^{12}) (x^{10})}{(x^{30})}$

Add the exponents in the numerator. $\frac{x^{22}}{x^{30}}$

Use the Quotient Property, $\frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}}$ . $\frac{1}{x^{8}}$

Your turn

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

Simplify: $\frac{{(a^{2})}^{3} {(a^{2})}^{4}}{{(a^{4})}^{5}} .$

How did it go?

PreviousDivide Monomials: example 6.69 Next Divide Monomials: example 6.71

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 6.5, 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.