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Algebra 1
Found in: Page 404
Algebra 1

Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

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Short Answer

Simplify the expression


The simplified version of 2g3h3gj42ghj2 is 18g7h3j10.

See the step by step solution

Step by Step Solution

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: xym=xmym

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: xmn=xm×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: xm×xn=xm+n

Step 4. Simplify the expression.

The given expression is: 2g3h3gj42ghj2

Apply the laws of indices and simplify.

2g3h3gj42ghj2=2g3h32g2j42g2h2j2 =2g3h9g2j4×2g2h2j2 =2g3h9g2j8g2h2j2 =2g3h9g2j8g2h2j2

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

2g3h3gj42ghj2=2g3h9g2j8g2h2j2 =2×9g3×g2×g2h×h2j8×j2 =18g3+2+2h1+2j8+2 =18g7h3j10

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