BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 20RE
To determine

To calculate: The simplified form of the expression, (a2)3(a3b)2(b3)4

Expert Solution

Answer to Problem 20RE

The simplified form of the expression is, (a)0(b)14=b14 .

Explanation of Solution

Given information:

The expression , (a2)3(a3b)2(b3)4

Formula used:

The algebraic identity:

  (am)n=amn(ab)n=anbnaman=amn .

And the factorization method.

Calculation:

Consider the expression, (a2)3(a3b)2(b3)4

  (a2)3(a3b)2(b3)4

Apply the identity:.. (am)n=amn .

  (a2)3(a3b)2(b3)4=(a)6a6b2b12

Apply the identity:

  aman=amn

  (a)6a6b2b12=(a)6+6(b)14=(a)o(b)14

Here,

  a0=1

  (a)o(b)14=1(b)14=(b)14

The above expression can’t be simplified further.

Thus, the simplified form of the expression is . , (a)0(b)14=b14

  

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