Evaluate 3^4-(2/5)^2*6

$3^{4} - {(\frac{2}{5})}^{2} \cdot 6$

Step 1

Simplify each term.

Raise $3$ to the power of $4$ .

$81 - {(\frac{2}{5})}^{2} \cdot 6$

Apply the product rule to $\frac{2}{5}$ .

$81 - \frac{2^{2}}{5^{2}} \cdot 6$

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

$81 - \frac{4}{5^{2}} \cdot 6$

Raise $5$ to the power of $2$ .

$81 - \frac{4}{25} \cdot 6$

Multiply $- \frac{4}{25} \cdot 6$ .

Multiply $6$ by $- 1$ .

$81 - 6 (\frac{4}{25})$

Combine $- 6$ and $\frac{4}{25}$ .

$81 + \frac{- 6 \cdot 4}{25}$

Multiply $- 6$ by $4$ .

$81 + \frac{- 24}{25}$

Move the negative in front of the fraction.

$81 - \frac{24}{25}$

Step 2

To write $81$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$81 \cdot \frac{25}{25} - \frac{24}{25}$

Step 3

Combine $81$ and $\frac{25}{25}$ .

$\frac{81 \cdot 25}{25} - \frac{24}{25}$

Step 4

Combine the numerators over the common denominator.

$\frac{81 \cdot 25 - 24}{25}$

Step 5

Simplify the numerator.

Multiply $81$ by $25$ .

$\frac{2025 - 24}{25}$

Subtract $24$ from $2025$ .

$\frac{2001}{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2001}{25}$

Decimal Form:

$80.04$

Mixed Number Form:

$80 \frac{1}{25}$