sqrt(x)^3 — step-by-step solution

Let's evaluate:

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

ⓘ A power of a power multiplies the exponents, (a^n)^m = a^(n*m):

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

x^{\frac{1}{2} \cdot 3}

x^{\frac{1}{2} \cdot 3}

ⓘ Multiplying a fraction by a number multiplies its numerator:

\frac{1}{2} \cdot 3

\frac{1 \cdot 3}{2}

\frac{3}{2}

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}

▶Result:

x \sqrt{x}