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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 153 (page 522)

Simplify ${(3 m^{2} n)}^{2} {(2 m n^{5})}^{4}$

Short Answer

Expert verified

Simplified expression is $144 m^{8} n^{22}$

Step by step solution

01

Step 1. Given information

${(3 m^{2} n)}^{2} {(2 m n^{5})}^{4}$

02

Step 2

Here

${(3 m^{2} n)}^{2} {(2 m n^{5})}^{4} = {(3)}^{2} {(m^{2})}^{2} {(n)}^{2} {(2)}^{4} {(m)}^{4} {(n^{5})}^{4} = 9 \times m^{2 \times 2} \times n^{2} \times 16 \times m^{4} \times n^{5 \times 4} = 144 \times m^{4} \times n^{2} \times m^{4} \times n^{20} = 144 \times m^{4 + 4} \times n^{2 + 20} = 144 m^{8} n^{22}$

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Most popular questions from this chapter

Simplify

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

Solve the square using the binomial squares pattern.

${(q + 12)}^{2}$

Use synthetic division to find the quotient and remainder.

$x^{3} - 3 x^{2} - 4 x + 12$ is divided by $x + 2$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(15 m^{2} - 8 n^{4}) (15 m^{2} + 8 n^{4})$

Write number (a) 57,000 (b) 0.026 in scientific notation

See all solutions

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