 # Simplify each expression (a) root(4)(3^2) (b) root(6)((x+1)^4) naivlingr 2021-01-15 Answered

Simplify each expression
(a) $\sqrt{{3}^{2}}$
(b) $\sqrt{{\left(x+1\right)}^{4}}$

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a) Definition:
If
Hence, if m is a positive integer, then
${a}^{m\text{/}n}={\left({a}^{1\text{/}n}\right)}^{m}$
are rational exponents of a.
Calculation:
From the above definition,
$\sqrt{{3}^{2}}$
$={\left({3}^{2}\right)}^{\frac{1}{4}}$
$={3}^{2×\frac{1}{4}}$
$={3}^{\frac{1}{2}}$
Answer: $\sqrt{3}$
b) Definition:
If
Hence, if m is a positive integer, then
${a}^{m\text{/}n}={\left({a}^{1\text{/}n}\right)}^{m}$
are rational exponents of a.
Calcucation:
$\sqrt{{\left(x+1\right)}^{4}}$
$={\left({\left(x+1\right)}^{4}\right)}^{\frac{1}{6}}$
$={\left(x+1\right)}^{4×\frac{1}{6}}$
Answer: ${\left(x+1\right)}^{\frac{2}{3}}$
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