CPM Homework Help : A2C Problem 12-13

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12-13.

What do you notice about the two problems below when you simplify them?

$\frac { x ^ { 1 / 2 } } { x ^ { - 3 / 2 } }$
Hint (a):
Use properties of exponents to simplify.
Step 1(a):
$\small x^{\frac{1}{2}} \cdot x^{\frac{3}{2}}$
Step 2(a):
$\small x^{\frac{4}{2}}$
Answer (a):
x²

$\sqrt { x } \div ( \frac { 1 } { \sqrt { x } } ) ^ { 3 }$
Step 1(b):
$\small x^{\frac{1}{2}}\div\left( x^{-\frac{1}{2}} \right)^3$
Step 2(b):
$\small \frac{x^{\frac{1}{2}}}{x^{-\frac{3}{2}}}$
Hint (b):
See part (a).

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