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 67E

(a)

To determine

To simplify: the given expression (8s3t3)23(s4t8)14 .

Expert Solution

Answer to Problem 67E

  (8s3t3)23(s4t8)14=4st4

Explanation of Solution

Given information:

Given expression

  (8s3t3)23(s4t8)14

Calculation:

Consider the given expression.

  (8s3t3)23(s4t8)14

Now, use the law of exponents, which states

  (am)n=amn and (ab)n=anbn

And combine like terms

  (8s3t3)23(s4t8)14=(23)23(s3)23(t3)23(s4)14(t8)14=(2)3×23(s)3×23(t)3×23(s)4×14(t)8×14=22s2t2st2=4st4 [an=1an]

Hence,

  (8s3t3)23(s4t8)14=4st4

(b)

To determine

To simplify: the given expression (32y5z10)15(64y6z12)16 .

Expert Solution

Answer to Problem 67E

  (32y5z10)15(64y6z12)16=4

Explanation of Solution

Given information:

Given expression

  (32y5z10)15(64y6z12)16

Calculation:

Consider the given expression.

  (32y5z10)15(64y6z12)16

Now, use the law of exponents, which states

  (am)n=amn and (ab)n=anbn

And combine like terms

  (32y5z10)15(64y6z12)16=(25)15(y5)15(z10)15(26)16(y6)16(z12)16=(2)5×15(y)5×15(z)10×15(2)6×(16)(y)6×(16)(z)(12)×(16)=2y1z221y1z2=2×112=4

Hence,

  (32y5z10)15(64y6z12)16=4

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