Simplify (4 1/2/4 3/4)^4

${(\frac{4 \frac{1}{2}}{4 \frac{3}{4}})}^{4}$

Convert $4 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

${(\frac{4 + \frac{1}{2}}{4 \frac{3}{4}})}^{4}$

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(\frac{4 \cdot \frac{2}{2} + \frac{1}{2}}{4 \frac{3}{4}})}^{4}$

Combine $4$ and $\frac{2}{2}$ .

${(\frac{\frac{4 \cdot 2}{2} + \frac{1}{2}}{4 \frac{3}{4}})}^{4}$

Combine the numerators over the common denominator.

${(\frac{\frac{4 \cdot 2 + 1}{2}}{4 \frac{3}{4}})}^{4}$

Simplify the numerator.

Multiply $4$ by $2$ .

${(\frac{\frac{8 + 1}{2}}{4 \frac{3}{4}})}^{4}$

Add $8$ and $1$ .

${(\frac{\frac{9}{2}}{4 \frac{3}{4}})}^{4}$

Convert $4 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

${(\frac{\frac{9}{2}}{4 + \frac{3}{4}})}^{4}$

Add $4$ and $\frac{3}{4}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

${(\frac{\frac{9}{2}}{4 \cdot \frac{4}{4} + \frac{3}{4}})}^{4}$

Combine $4$ and $\frac{4}{4}$ .

${(\frac{\frac{9}{2}}{\frac{4 \cdot 4}{4} + \frac{3}{4}})}^{4}$

Combine the numerators over the common denominator.

${(\frac{\frac{9}{2}}{\frac{4 \cdot 4 + 3}{4}})}^{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

${(\frac{\frac{9}{2}}{\frac{16 + 3}{4}})}^{4}$

Add $16$ and $3$ .

${(\frac{\frac{9}{2}}{\frac{19}{4}})}^{4}$

Multiply the numerator by the reciprocal of the denominator.

${(\frac{9}{2} \cdot \frac{4}{19})}^{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

${(\frac{9}{2} \cdot \frac{2 (2)}{19})}^{4}$

Cancel the common factor.

${(\frac{9}{2} \cdot \frac{2 \cdot 2}{19})}^{4}$

Rewrite the expression.

${(9 (\frac{2}{19}))}^{4}$

Combine $9$ and $\frac{2}{19}$ .

${(\frac{9 \cdot 2}{19})}^{4}$

Simplify the expression.

Multiply $9$ by $2$ .

${(\frac{18}{19})}^{4}$

Apply the product rule to $\frac{18}{19}$ .

$\frac{18^{4}}{19^{4}}$

Raise $18$ to the power of $4$ .

$\frac{104976}{19^{4}}$

Raise $19$ to the power of $4$ .

$\frac{104976}{130321}$

The result can be shown in multiple forms.

Exact Form:

$\frac{104976}{130321}$

Decimal Form:

$0.80551868 \dots$

Simplify (4 1/2/4 3/4)^4

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