Ayaana Buck

2020-11-29

To simplify:

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

The given expression

Dora

Skilled2020-11-30Added 98 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,

$\sqrt{s\sqrt{{s}^{3}}}$

By using the law of exponents,

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

$={(s\cdot \text{}{s}^{\frac{3}{2}})}^{\frac{1}{2}}$

Apply exponent rule:${a}^{b}\cdot \text{}{a}^{c}={a}^{b+c},$ we get

$={\left({s}^{\frac{5}{2}}\right)}^{\frac{1}{2}}$

Apply exponent rule:${\left({a}^{b}\right)}^{c}={a}^{bc},$ we get

$={s}^{\frac{5}{2}\cdot \frac{1}{2}}$

$={s}^{\frac{5}{4}}$

Final Statement:

The simplified form of$\sqrt{s\sqrt{{s}^{3}}}$ is $s}^{\frac{5}{4}$

Law of exponents:

For any rational exponent

If n is even, then we require that

Step 2

Consider the given expression,

By using the law of exponents,

Apply exponent rule:

Apply exponent rule:

Final Statement:

The simplified form of