Write the Fraction in Simplest Form ((125^2)/125 4/3)

$(\frac{125^{2}}{125 \frac{4}{3}})$

Step 1

Convert $125 \frac{4}{3}$ to an improper fraction.

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

$(\frac{125^{2}}{125 + \frac{4}{3}})$

Add $125$ and $\frac{4}{3}$ .

To write $125$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{125^{2}}{125 \cdot \frac{3}{3} + \frac{4}{3}})$

Combine $125$ and $\frac{3}{3}$ .

$(\frac{125^{2}}{\frac{125 \cdot 3}{3} + \frac{4}{3}})$

Combine the numerators over the common denominator.

$(\frac{125^{2}}{\frac{125 \cdot 3 + 4}{3}})$

Simplify the numerator.

Multiply $125$ by $3$ .

$(\frac{125^{2}}{\frac{375 + 4}{3}})$

Add $375$ and $4$ .

$(\frac{125^{2}}{\frac{379}{3}})$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(125^{2} \frac{3}{379})$

Step 3

Raise $125$ to the power of $2$ .

$(15625 (\frac{3}{379}))$

Step 4

Multiply $15625 (\frac{3}{379})$ .

Combine $15625$ and $\frac{3}{379}$ .

$(\frac{15625 \cdot 3}{379})$

Multiply $15625$ by $3$ .

$(\frac{46875}{379})$