Solve [(-3)(-3)(-3)(-3)(-3)(-3)(-3)(-3)/(-3)^15div(-3)^10]^3

$$[ \frac { ( - 3 ) ( - 3 ) ( - 3 ) ( - 3 ) ( - 3 ) ( - 3 ) ( - 3 ) ( - 3 ) } { ( - 3 ) ^ { 15 } \div ( - 3 ) ^ { 10 } } ] ^ { 3 }$$

Evaluate

$$-19683$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 15 to get 5.

$$\left(\frac{-3\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)}{\left(-3\right)^{5}}\right)^{3}$$

Cancel out -3\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right) in both numerator and denominator.

$$\left(-3\left(-3\right)\left(-3\right)\right)^{3}$$

Multiply -3 and -3 to get 9.

$$\left(9\left(-3\right)\right)^{3}$$

Multiply 9 and -3 to get -27.

$$\left(-27\right)^{3}$$

Calculate -27 to the power of 3 and get -19683.

$$-19683$$

Factor

$$-19683$$