Solve [(-2/5bc)^3]^2:(-2/5bc)^7}

$$[ ( - \frac { 2 } { 5 } b c ) ^ { 3 } ] ^ { 2 } : ( - \frac { 2 } { 5 } b c ) ^ { 7 } \}$$

Evaluate

$$-\frac{5}{2bc}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(-\frac{2}{5}bc\right)^{6}}{\left(-\frac{2}{5}bc\right)^{7}}$$

Rewrite \left(-\frac{2}{5}bc\right)^{7} as \left(-\frac{2}{5}bc\right)^{6}\left(-\frac{2}{5}\right)bc. Cancel out \left(-\frac{2}{5}bc\right)^{6} in both numerator and denominator.

$$\frac{1}{-\frac{2}{5}bc}$$

Expand

$$-\frac{5}{2bc}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(-\frac{2}{5}bc\right)^{6}}{\left(-\frac{2}{5}bc\right)^{7}}$$

Rewrite \left(-\frac{2}{5}bc\right)^{7} as \left(-\frac{2}{5}bc\right)^{6}\left(-\frac{2}{5}\right)bc. Cancel out \left(-\frac{2}{5}bc\right)^{6} in both numerator and denominator.

$$\frac{1}{-\frac{2}{5}bc}$$