Find out the answer to "Evaluate each expression. P(14,0)"

nicekikah

Answered question

2021-08-06

Evaluate each expression.
P(14,0)

Answer & Explanation

AGRFTr

Skilled2021-08-07Added 95 answers

Solution below

user_27qwe

Skilled2021-12-09Added 375 answers

Simplify the following:
a) $\sqrt{\frac{4}{9}}$

Hint: For all $n \geq 0, \sqrt{\frac{m}{n}} = \frac{\sqrt{m}}{\sqrt{n}} .$
$\sqrt{\frac{4}{9}} = \frac{\sqrt{4}}{\sqrt{9}} :$
$\frac{\sqrt{4}}{\sqrt{9}}$

Hint: Simplify radicals.
$\sqrt{9} = \sqrt{3^{2}} = 3 :$
$\frac{\sqrt{4}}{3}$

Hint: Simplify radicals.
$\sqrt{4} = \sqrt{2^{2}} = 2 :$
Answer: $\frac{2}{3}$

b) $\sqrt[4]{256}$

Rewrite $256$ as $4^{4}$

$\sqrt[4]{4^{4}}$

Pull terms out from under the radical, assuming positive real numbers.4

Simplify the following:
${(\frac{1}{64})}^{\frac{1}{4}}$

Hint: | For all $n \geq 0, {(\frac{m}{n})}^{\frac{1}{4}} = \frac{m^{\frac{1}{4}}}{n^{\frac{1}{4}}} .$
${(\frac{1}{64})}^{\frac{1}{4}} = \frac{1^{\frac{1}{4}}}{64^{\frac{1}{4}}} :$
$\frac{1^{\frac{1}{4}}}{64^{\frac{1}{4}}}$

Hint: Simplify radicals.
$64^{\frac{1}{4}} = {(2^{6})}^{\frac{1}{4}} = 2 \sqrt{2} :$
$\frac{1^{\frac{1}{4}}}{2 \sqrt{2}}$

Hint: One raised to any number is one.
$1^{\frac{1}{4}} = 1 :$
$\frac{1}{2 \sqrt{2}}$

Hint: Multiply numerator and denominator of $\frac{1}{2 \sqrt{2}}$ by $\sqrt{2} .$
Rationalize the denominator. $\frac{1}{2 \sqrt{2}} = \frac{1}{2 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2 \times 2} :$
$\frac{\sqrt{2}}{2 \times 2}$

Hint: Multiply 2 and 2 together.
$2 \times 2 = 4 :$
Answer: $\frac{\sqrt{2}}{4}$

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