Simplify ((54^(1/2))^(5/3))/(54^(1/2))

$\frac{{(54^{\frac{1}{2}})}^{\frac{5}{3}}}{54^{\frac{1}{2}}}$

Multiply the exponents in ${(54^{\frac{1}{2}})}^{\frac{5}{3}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{54^{\frac{1}{2} \cdot \frac{5}{3}}}{54^{\frac{1}{2}}}$

Multiply $\frac{1}{2} \cdot \frac{5}{3}$ .

Multiply $\frac{1}{2}$ by $\frac{5}{3}$ .

$\frac{54^{\frac{5}{2 \cdot 3}}}{54^{\frac{1}{2}}}$

Multiply $2$ by $3$ .

$\frac{54^{\frac{5}{6}}}{54^{\frac{1}{2}}}$

Move $54^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$54^{\frac{5}{6}} \cdot 54^{- \frac{1}{2}}$

Multiply $54^{\frac{5}{6}}$ by $54^{- \frac{1}{2}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$54^{\frac{5}{6} - \frac{1}{2}}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$54^{\frac{5}{6} - \frac{1}{2} \cdot \frac{3}{3}}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$54^{\frac{5}{6} - \frac{3}{2 \cdot 3}}$

Multiply $2$ by $3$ .

$54^{\frac{5}{6} - \frac{3}{6}}$

Combine the numerators over the common denominator.

$54^{\frac{5 - 3}{6}}$

Subtract $3$ from $5$ .

$54^{\frac{2}{6}}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$54^{\frac{2 (1)}{6}}$

Cancel the common factors.

Factor $2$ out of $6$ .

$54^{\frac{2 \cdot 1}{2 \cdot 3}}$

Cancel the common factor.

$54^{\frac{2 \cdot 1}{2 \cdot 3}}$

Rewrite the expression.

$54^{\frac{1}{3}}$

The result can be shown in multiple forms.

Exact Form:

$54^{\frac{1}{3}}$

Decimal Form:

$3.77976314 \dots$