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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