To simplify:

The given expression$\sqrt{{x}^{3}}$

The given expression

Jaden Easton
2020-11-29
Answered

To simplify:

The given expression$\sqrt{{x}^{3}}$

The given expression

You can still ask an expert for help

grbavit

Answered 2020-11-30
Author has **109** answers

Step 1

Law of exponents:

For any rational exponent$\frac{m}{n}$ in lowest terms, where m and n are integers and $n>0,$ we define

$a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}=\sqrt{n}\left\{{a}^{m}\right\$

If n is even, then we require that$a\ge 0$

Step 2

Consider the given expression,

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

Apply Law of exponents$a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}=\sqrt{n}\left\{{a}^{m}\right\$ we get,

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

Therefore the expression$\sqrt{{x}^{3}}$ simplifies to $x}^{\frac{3}{2}$

Final Statement:

The simplified form of$\sqrt{{x}^{3}}$ is $x}^{\frac{3}{2}$

Law of exponents:

For any rational exponent

If n is even, then we require that

Step 2

Consider the given expression,

Apply Law of exponents

Therefore the expression

Final Statement:

The simplified form of

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That is, I would like to solve for the coefficients ${p}_{2},{p}_{1},{p}_{0},{q}_{1},{q}_{0}$. Note that $\mathrm{d}\mathrm{e}\mathrm{g}(p)\le 2$ and $\mathrm{d}\mathrm{e}\mathrm{g}(q)\le 1$.

I don't know where to begin, so I'm looking for suggestions on how to approach this problem; pointers to relevant numerical methods would also be greatly appreciated

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