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Exercises Polynomials and factoring

Example 10.68 from Prealgebra, 10.5 Integer Exponents and Scientific Notation

Integer Exponents and Scientific Notation: example 10.68

Simplify:

ⓐ $x^{−4} \cdot x^{6}$
ⓑ $y^{−6} \cdot y^{4}$
ⓒ $z^{−5} \cdot z^{−3}$

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

ⓐ

$x^{−4} \cdot x^{6}$

Use the Product Property, $a^{m} \cdot a^{n} = a^{m + n} .$ $x^{−4 + 6}$

Simplify. $x^{2}$

ⓑ

$y^{−6} \cdot y^{4}$

The bases are the same, so add the exponents. $y^{−6 + 4}$

Simplify. $y^{−2}$

Use the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}} .$ $\frac{1}{y^{2}}$

ⓒ

$z^{−5} \cdot z^{−3}$

The bases are the same, so add the exponents. $z^{−5−3}$

Simplify. $z^{−8}$

Use the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}} .$ $\frac{1}{z^{8}}$

Your turn

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

Simplify:

ⓐ $x^{−3} \cdot x^{7}$
ⓑ $y^{−7} \cdot y^{2}$
ⓒ $z^{−4} \cdot z^{−5}$

How did it go?

PreviousInteger Exponents and Scientific Notation: example 10.67 Next Integer Exponents and Scientific Notation: example 10.69

From Prealgebra (1st edition) by OpenStax (Rice University), section 10.5, 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.