Solve =[(-3)^{2}*(-3)^10:(-3)^9]^3:(-3)^7

$$= [ ( - 3 ) ^ { 2 } \cdot ( - 3 ) ^ { 10 } : ( - 3 ) ^ { 9 } ] ^ { 3 } : ( - 3 ) ^ { 7 }$$

Evaluate

$$9$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$\frac{\left(\frac{\left(-3\right)^{12}}{\left(-3\right)^{9}}\right)^{3}}{\left(-3\right)^{7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 9 from 12 to get 3.

$$\frac{\left(\left(-3\right)^{3}\right)^{3}}{\left(-3\right)^{7}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-3\right)^{9}}{\left(-3\right)^{7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 9 to get 2.

$$\left(-3\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$9$$

Factor

$$3^{2}$$