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Exercises Polynomials and factoring

Example 10.65 from Prealgebra, 10.5 Integer Exponents and Scientific Notation

Integer Exponents and Scientific Notation: example 10.65

Simplify:

ⓐ $4 \cdot 2^{−1}$
ⓑ ${(4 \cdot 2)}^{−1}$

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
Remember to always follow the order of operations.

ⓐ

Do exponents before multiplication. $4 \cdot 2^{−1}$

Use $a^{- n} = \frac{1}{a^{n}} .$ $4 \cdot \frac{1}{2^{1}}$

Simplify. $2$

ⓑ ${(4 \cdot 2)}^{−1}$

Simplify inside the parentheses first. ${(8)}^{−1}$

Use $a^{- n} = \frac{1}{a^{n}} .$ $\frac{1}{8^{1}}$

Simplify. $\frac{1}{8}$

Your turn

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

Simplify:

ⓐ $6 \cdot 3^{−1}$
ⓑ ${(6 \cdot 3)}^{−1}$

How did it go?

PreviousInteger Exponents and Scientific Notation: example 10.64 Next Integer Exponents and Scientific Notation: example 10.66

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.