naivlingr

2021-01-15

Simplify each expression

(a)

(b)

Ayesha Gomez

Skilled2021-01-16Added 104 answers

a) Definition:

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

Hence, if m is a positive integer, then

$a}^{m\text{/}n}={\left({a}^{1\text{/}n}\right)}^{m$

$1\text{/}n\text{}\text{and}\text{}{\displaystyle m\text{/}n}$ are rational exponents of a.

Calculation:

From the above definition,

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

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

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

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

Answer:$\sqrt{3}$

b) Definition:

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

Hence, if m is a positive integer, then

$a}^{m\text{/}n}={\left({a}^{1\text{/}n}\right)}^{m$

$1/n\text{}\text{and}\text{}m/n$ are rational exponents of a.

Calcucation:

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

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

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

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

If

Hence, if m is a positive integer, then

Calculation:

From the above definition,

Answer:

b) Definition:

If

Hence, if m is a positive integer, then

Calcucation:

Answer:

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

22+64

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