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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 160 (page 522)

Simplify $\frac{{(- 4 m^{- 3})}^{2} {(5 m^{4})}^{3}}{{(- 10 m^{6})}^{3}}$

Short Answer

Expert verified

Simplified expression is $- 2 m^{- 12}$

Step by step solution

01

Given information

Simplify $\frac{{(- 4 m^{- 3})}^{2} {(5 m^{4})}^{3}}{{(- 10 m^{6})}^{3}}$

02

Simplification

Here

$\frac{{(- 4 m^{- 3})}^{2} {(5 m^{4})}^{3}}{{(- 10 m^{6})}^{3}} = \frac{{(- 4)}^{2} {(m^{- 3})}^{2} {(5)}^{3} {(m^{4})}^{3}}{{(- 10)}^{3} {(m^{6})}^{3}} = \frac{16 m^{- 6} \times 125 m^{12}}{- 1000 m^{18}} = - 2 m^{- 6 + 12 - 18} = - 2 m^{- 12}$

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Most popular questions from this chapter

In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method

$(7 q + 4) (3 q - 8)$

Use synthetic division to find the quotient and remainder.

$x^{3} - 6 x^{2} + 5 x + 14$ is divided by $x + 1$

Convert (a) $- 8.3 \times 10^{2}$ (b) $3.8 \times 10^{- 2}$ to decimal form.

$Find the :difference (9 b^{2} - 5 b - 4) - (3 b^{2} - 5 b - 7)$

Simplify

(a) ${(2 r^{- 2})}^{3} {(4^{- 1} r)}^{2}$ (b) ${(3 x^{- 3})}^{3} {(3^{- 1} x^{5})}^{4}$

See all solutions

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