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 1.2, Problem 70E

(a)

To determine

To simplify: the given expression (a16b3x1y)3(x2b1a32y13) .

Expert Solution

Answer to Problem 70E

  (a16b3x1y)3(x2b1a32y13)=xab10y103

Explanation of Solution

Given information:

Given expression

  (a16b3x1y)3(x2b1a32y13)

Calculation:

Consider the given expression.

  (a16b3x1y)3(x2b1a32y13)

Now, use the law of exponents, which states

  (am)n=amn , (ab)n=anbn and (ab)n=anbn

And combine like terms

  (a16b3x1y)3(x2b1a32y13)=(a16)3(b3)3(x1)3(y)3(x2b1a32y13)=a12b9x3y3(x2b1a32y13)=x2+3y313b91a1232 [aman=am+n,aman=amn]=x1y103b10a1=xab10y103 [an=1an]

Hence,

  (a16b3x1y)3(x2b1a32y13)=xab10y103

(b)

To determine

To simplify: the given expression (9st)32(27s3t4)23(3s24t13)1 .

Expert Solution

Answer to Problem 70E

  (9st)32(27s3t4)23(3s24t13)1=4s32t92

Explanation of Solution

Given information:

Given expression

  (9st)32(27s3t4)23(3s24t13)1

Calculation:

Consider the given expression.

  (9st)32(27s3t4)23(3s24t13)1

Now, use the law of exponents, which states

  (am)n=amn , (ab)n=anbn and (ab)n=anbn

And combine like terms

  (9st)32(27s3t4)23(3s24t13)1=(9)32s32t32(27)23(s3)23(t4)2331(s2)141(t13)1=27s32t329s2t234s23t13=4s32t32+3 [aman=am+n]=4s32t92

Hence,

  (9st)32(27s3t4)23(3s24t13)1=4s32t92

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