Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q19.

Expert-verified

Algebra 1

Found in: Page 404

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Simplify the expression
$(- 2 g^{3} h) {(- 3 g j^{4})}^{2} {(- g h j)}^{2}$

The simplified version of $(- 2 g^{3} h) {(- 3 g j^{4})}^{2} {(- g h j)}^{2}$ is $- 18 g^{7} h^{3} j^{10}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the product power law of ‘laws of indices’.

According to this law, when a product is raised to a power, every factor of the product is raised to the power.

In general: ${(x y)}^{m} = x^{m} y^{m}$

Step 2. State the ‘Law of indices’ for power of index numbers.

If a term with a power is itself raised to a power then the powers are multiplied together.

In general: ${(x^{m})}^{n} = x^{m \times n}$

Step 3. State the multiplication rule of Law of indices.

If the two terms have the same base (in this case x) and are to be multiplied together, then their indices are added.

In general: $x^{m} \times x^{n} = x^{m + n}$

Step 4. Simplify the expression.

The given expression is: $(- 2 g^{3} h) {(- 3 g j^{4})}^{2} {(- g h j)}^{2}$

Apply the laws of indices and simplify.

$(- 2 g^{3} h) {(- 3 g j^{4})}^{2} {(- g h j)}^{2} = (- 2 g^{3} h) [{(- 3)}^{2} {(g)}^{2} {(j^{4})}^{2}] [{(- g)}^{2} {(h)}^{2} {(j)}^{2}] = (- 2 g^{3} h) [9 g^{2} (j^{4 \times 2})] (g^{2} h^{2} j^{2}) = (- 2 g^{3} h) [9 g^{2} (j^{8})] (g^{2} h^{2} j^{2}) = (- 2 g^{3} h) (9 g^{2} j^{8}) (g^{2} h^{2} j^{2})$

Collect the like terms together and use multiplication rule to simplify further.

$(- 2 g^{3} h) {(- 3 g j^{4})}^{2} {(- g h j)}^{2} = (- 2 g^{3} h) (9 g^{2} j^{8}) (g^{2} h^{2} j^{2}) = (- 2 \times 9) (g^{3} \times g^{2} \times g^{2}) (h \times h^{2}) (j^{8} \times j^{2}) = (- 18) (g^{3 + 2 + 2}) (h^{1 + 2}) (j^{8 + 2}) = - 18 g^{7} h^{3} j^{10}$

Most popular questions for Math Textbooks

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

At a family fun centre, the Wilson and Sanchez families each bought video game tokens and batting cage tokens as shown in the table.

Family	Wilson	Sanchez
Number of Video Game Tokens	25	30
Number of Batting Cage Tokens	8	6
Total Cost	$$ 26.50$	$$ 25.50$

What is the cost in dollars of a batting cage token at the family fun centre?

Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial.

$2 x^{- 3} - 4 x + 1$

Write three different expressions that can be simplified to $x^{6}$ .

Choose a term from the Key Vocabulary list above that best describes the given expression.

$(x + 2) (x - 5) = x^{2} - 3 x - 10$

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

122

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free