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 44E

(a)

To determine

To simplify: given expression (s2t2)2(s2t)3 .

Expert Solution

Answer to Problem 44E

  (s2t2)2(s2t)3=s2t7

Explanation of Solution

Given information:

Given expression

  (s2t2)2(s2t)3

Calculation:

Consider the given expression.

  (s2t2)2(s2t)3

Now. Simplify using law of exponents (ab)n=anbn and (am)n=amn .

  (s2t2)2(s2t)3={(s2)2(t2)2}{(s2)3(t)3}=(s4t4)(s6t3)

To simplify this, rewrite the above expression as a single product.

  (s4t4)(s6t3)=s4s6t4t3

Now, use the first law of exponents, which states

  aman=am+n

And combine like terms

  s4s6t4t3=s4+6t4+3=s2t7

Hence,

  (s2t2)2(s2t)3=s2t7

(b)

To determine

To evaluate: the given expression (2u2v3)3(3u3v)3 .

Expert Solution

Answer to Problem 44E

  (2u2v3)3(3u3v)3=216v12u3

Explanation of Solution

Given information:

Given expression

  (2u2v3)3(3u3v)3

Calculation:

Consider the given expression.

  (2u2v3)3(3u3v)3

Now. Simplify using law of exponents (ab)n=anbn and (am)n=amn .

  (2u2v3)3(3u3v)3={23(u2)3(v3)3}{33(u3)3(v)3}=(23u6v9)(33u9v3)

To simplify this, first rewrite the above expression as a single product.

  (23u6v9)(33u9v3)=2333u6u9v9v3=216u6u9v9v3

Now, use the first law of exponents, which states

  aman=am+n

And combine like terms

  216u6u9v9v3=216u69v9+3=216u3v12

Hence,

  (2u2v3)3(3u3v)3=216v12u3

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