CB-MA007-261013: Multiplication Properties of Exponents

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Let's consider monomials with more than one variable. The rules are the same; the problems just become more interesting. Instead of just doing $$x^2*x^3$$ to get $$x^5$$, we now get to do things like $$x^3y^4*x^2y^6$$ to get $x^5*y^{10}$. After you read, complete example 6.27 and check your answer.

Multiply Monomials

Since a monomial is an algebraic expression, we can use the properties of exponents to multiply monomials.

Example 6.26

Multiply: $\left(3 x^{2}\right)\left(-4 x^{3}\right)$.

Solution

	$\left(3 x^{2}\right)\left(-4 x^{3}\right)$
Use the Commutative Property to rearrange the terms.	$3 \cdot(-4) \cdot x^{2} \cdot x^{3}$
Multiply.	$-12 x^{5}$

Try It 6.51

Multiply: $\left(5 y^{7}\right)\left(-7 y^{4}\right)$.

Try It 6.52

Multiply: $\left(-6 b^{4}\right)\left(-9 b^{5}\right)$.

Example 6.27

Multiply: $\left(\frac{5}{6} x^{3} y\right)\left(12 x y^{2}\right)$.

Solution

	$\left(\frac{5}{6} x^{3} y\right)\left(12 x y^{2}\right)$
Use the Commutative Property to rearrange the terms.	$\frac{5}{6} \cdot 12 \cdot x^{3} \cdot x \cdot y \cdot y^{2}$
Multiply.	$10 x^{4} y^{3}$

Try It 6.53

Multiply: $$(\frac{2}{5}a^4b^3)(15ab^3)$$.

Try It 6.54

Multiply: $$(\frac{2}{3}r^5s)(12r^6s^7)$$.

Source: OpenStax, https://openstax.org/books/elementary-algebra/pages/6-2-use-multiplication-properties-of-exponents
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	\(\left(3 x^{2}\right)\left(-4 x^{3}\right)\)
Use the Commutative Property to rearrange the terms.	\(3 \cdot(-4) \cdot x^{2} \cdot x^{3}\)
Multiply.	\(-12 x^{5}\)

	\(\left(\frac{5}{6} x^{3} y\right)\left(12 x y^{2}\right)\)
Use the Commutative Property to rearrange the terms.	\(\frac{5}{6} \cdot 12 \cdot x^{3} \cdot x \cdot y \cdot y^{2}\)
Multiply.	\(10 x^{4} y^{3}\)