Algebra Examples

${(\frac{2}{5})}^{- 3} \cdot {(\frac{3}{7})}^{- 3}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{5}{2})}^{3} \cdot {(\frac{3}{7})}^{- 3}$

Step 2

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

$\frac{5^{3}}{2^{3}} \cdot {(\frac{3}{7})}^{- 3}$

Step 3

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

$\frac{125}{2^{3}} \cdot {(\frac{3}{7})}^{- 3}$

Step 4

Raise $2$ to the power of $3$ .

$\frac{125}{8} \cdot {(\frac{3}{7})}^{- 3}$

Step 5

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{125}{8} \cdot {(\frac{7}{3})}^{3}$

Step 6

Apply the product rule to $\frac{7}{3}$ .

$\frac{125}{8} \cdot \frac{7^{3}}{3^{3}}$

Step 7

Combine.

$\frac{125 \cdot 7^{3}}{8 \cdot 3^{3}}$

Step 8

Simplify the expression.

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Step 8.1

Raise $7$ to the power of $3$ .

$\frac{125 \cdot 343}{8 \cdot 3^{3}}$

Step 8.2

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

$\frac{125 \cdot 343}{8 \cdot 27}$

Step 8.3

Multiply $125$ by $343$ .

$\frac{42875}{8 \cdot 27}$

Step 8.4

Multiply $8$ by $27$ .

$\frac{42875}{216}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{42875}{216}$

Decimal Form:

$198.495\overline{370}$

Mixed Number Form:

$198 \frac{107}{216}$