CPM Homework Help : CCA2 Problem 10-129

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10-129.

Use properties of exponents to rewrite each expression below so that it involves only multiplication and exponents.

$\frac { ( - 2 x ) ^ { 3 } y z ^ { 2 } } { 2 ^ { - 1 } \sqrt { x } y ^ { - 3 } }$
Step 1(a):
$\frac{(-2)^3x^3y^1z^2}{2^{-1}x^\frac{1}{2}y^{-3}$}$
Step 2(a):
$\frac{-2^3x^3y^1z^2}{2^{-1}x^\frac{1}{2}y^{-3}}$
Step 3(a):
Now apply the exponent rule for division.

$\frac { 3 x ^ { 2 } y ^ { 3 } } { \sqrt { 3 x } \sqrt [ 3 ] { y } }$
Answer (b):
$3^\frac{1}{2}x^\frac{3}{2}y^\frac{8}{3}$

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