To simplify: The given expression sqrt{x^{3}}

Question

To simplify:
The given expression

\sqrt{x^{3}}

Answer 1

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}} = {(\sqrt{n} {a})}^{m} = \sqrt{n} {a^{m}}

If n is even, then we require that

a \geq 0

Step 2
Consider the given expression,

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

Apply Law of exponents

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

we get,

{(x^{3})}^{\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}}

Expert Answer