CPM Homework Help : APCALC Problem 1-41

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1-41.

Wei Kit knows that radical expressions can be rewritten using rational exponents. Study his examples below.

Examples: $\sqrt{x}=x^{1/2 }$ $( \sqrt [ 5 ] { z } ) ^ { 2 }= z^{2/5}$ $\sqrt [ 3 ] { m ^ { 2 } } = m^{2/3}$

Rewrite the following radicals expressions with rational exponents.

$\sqrt { k ^ { 7 } }$
Answer (a):
$\small k^{\frac{1}{7}}$

$\sqrt [ 3 ] { t ^ { 4 } }$
Hint (b):
Reread the examples above.

$( \sqrt { n } ) ^ { 4 }$
Hint (c):
$\text{Recall: } \left(\sqrt{n}\right)^4=\left(n^{\frac{1}{2}}\right)^{4}$
Now simplify.

$\sqrt [ 5 ] { b ^ { 31 } }$
Hint (d):
Reread the examples above.

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