simplify (x^2)/(sqrt(x)) — step-by-step solution

Let's reduce:

\frac{x^{2}}{\sqrt{x}}

ⓘ The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor:

\frac{x^{2}}{\sqrt{x}}

x^{2 - \frac{1}{2}}

x^{2 - \frac{1}{2}}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

2 - \frac{1}{2}

\frac{2 \cdot 2 - 1}{2}

x^{\frac{2 \cdot 2 - 1}{2}}

ⓘ Multiplications are done before additions and subtractions:

2 \cdot 2

4

x^{\frac{4 - 1}{2}}

ⓘ The numerator and the denominator are computed before the division:

4 - 1

3

x^{\frac{3}{2}}

ⓘ Split the exponent:

\frac{3}{2}

\frac{2}{2}

\frac{1}{2}

1

\frac{1}{2}

■For

x

≥ 0, a sum of exponents gives a product of powers:

x^{1 + \frac{1}{2}}

x x^{\frac{1}{2}}

, and exponent 1/2 means the square root:

x^{\frac{1}{2}}

\sqrt{x}

In the reals, for

x

≥ 0, exponent

\frac{3}{2}

means a square root followed by a power:

x^{\frac{3}{2}}

x \sqrt{x}

▶Simplified form:

x \sqrt{x}