Evaluate ((4/5)^3*(4/5)^2)-11/5

$({(\frac{4}{5})}^{3} \cdot {(\frac{4}{5})}^{2}) - \frac{11}{5}$

Step 1

Simplify each term.

Multiply ${(\frac{4}{5})}^{3}$ by ${(\frac{4}{5})}^{2}$ by adding the exponents.

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

${(\frac{4}{5})}^{3 + 2} - \frac{11}{5}$

Add $3$ and $2$ .

${(\frac{4}{5})}^{5} - \frac{11}{5}$

Apply the product rule to $\frac{4}{5}$ .

$\frac{4^{5}}{5^{5}} - \frac{11}{5}$

Raise $4$ to the power of $5$ .

$\frac{1024}{5^{5}} - \frac{11}{5}$

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

$\frac{1024}{3125} - \frac{11}{5}$

Step 2

To write $- \frac{11}{5}$ as a fraction with a common denominator, multiply by $\frac{625}{625}$ .

$\frac{1024}{3125} - \frac{11}{5} \cdot \frac{625}{625}$

Step 3

Write each expression with a common denominator of $3125$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{5}$ by $\frac{625}{625}$ .

$\frac{1024}{3125} - \frac{11 \cdot 625}{5 \cdot 625}$

Multiply $5$ by $625$ .

$\frac{1024}{3125} - \frac{11 \cdot 625}{3125}$

Step 4

Combine the numerators over the common denominator.

$\frac{1024 - 11 \cdot 625}{3125}$

Step 5

Simplify the numerator.

Multiply $- 11$ by $625$ .

$\frac{1024 - 6875}{3125}$

Subtract $6875$ from $1024$ .

$\frac{- 5851}{3125}$

Step 6

Move the negative in front of the fraction.

$- \frac{5851}{3125}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{5851}{3125}$

Decimal Form:

$- 1.87232$

Mixed Number Form:

$- 1 \frac{2726}{3125}$