Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Multiply $2$ by $3$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $3$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Subtract $3$ from $5$ .

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

Step 3.6

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

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Step 3.6.1

Factor $2$ out of $2$ .

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

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $2$ out of $6$ .

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

Step 3.6.2.2

Cancel the common factor.

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

Step 3.6.2.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.77976314 \dots$