Best solutions to - "Simplify each expression (a) 324 (b) (x+1)46"

naivlingr

Answered question

2021-01-15

Simplify each expression
(a) $\sqrt[4]{3^{2}}$
(b) $\sqrt[6]{{(x + 1)}^{4}}$

Ayesha Gomez

Skilled2021-01-16Added 104 answers

a) Definition:
If

a = real number and n = positive integer such that the principal nth \sqrt{} of a exists, then a^{1 / n} is defined as a^{1 / n} = \sqrt[n]{a}

Hence, if m is a positive integer, then

a^{m / n} = {(a^{1 / n})}^{m}

1 / n and m / n

are rational exponents of a.
Calculation:
From the above definition,

\sqrt[4]{3^{2}}

= {(3^{2})}^{\frac{1}{4}}

= 3^{2 \times \frac{1}{4}}

= 3^{\frac{1}{2}}

Answer:

\sqrt{3}

b) Definition:
If

a = real number and n = positive integer such that the principal nth \sqrt{} of a exists, then a^{1 / n} is defined as a^{1 / n} = \sqrt[n]{a}

Hence, if m is a positive integer, then

a^{m / n} = {(a^{1 / n})}^{m}

1 / n and m / n

are rational exponents of a.
Calcucation:

\sqrt[6]{{(x + 1)}^{4}}

= {({(x + 1)}^{4})}^{\frac{1}{6}}

= {(x + 1)}^{4 \times \frac{1}{6}}

Answer:

{(x + 1)}^{\frac{2}{3}}

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

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