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

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Raise $5$ to the power of $3$ .

$5 {(125 (\frac{5}{2}))}^{2}$

Step 3

Multiply $125 (\frac{5}{2})$ .

Combine $125$ and $\frac{5}{2}$ .

$5 {(\frac{125 \cdot 5}{2})}^{2}$

Multiply $125$ by $5$ .

$5 {(\frac{625}{2})}^{2}$

$5 {(\frac{625}{2})}^{2}$

Step 4

Apply the product rule to $\frac{625}{2}$ .

$5 \frac{625^{2}}{2^{2}}$

Step 5

Raise $625$ to the power of $2$ .

$5 \frac{390625}{2^{2}}$

Step 6

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

$5 (\frac{390625}{4})$

Step 7

Multiply $5 (\frac{390625}{4})$ .

Combine $5$ and $\frac{390625}{4}$ .

$\frac{5 \cdot 390625}{4}$

Multiply $5$ by $390625$ .

$\frac{1953125}{4}$

$\frac{1953125}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1953125}{4}$

Decimal Form:

$488281.25$

Mixed Number Form:

$488281 \frac{1}{4}$

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