Solve frac{(-9)^{11}*(-9)^-7}{3^4}*3^3:(1/3)^-7

$$\frac { ( - 9 ) ^ { 11 } \times ( - 9 ) ^ { - 7 } } { 3 ^ { 4 } } \times 3 ^ { 3 } : ( \frac { 1 } { 3 } ) ^ { - 7 }$$

Evaluate

$$1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 11 and -7 to get 4.

$$\frac{\frac{\left(-9\right)^{4}}{3^{4}}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate -9 to the power of 4 and get 6561.

$$\frac{\frac{6561}{3^{4}}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{6561}{81}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Divide 6561 by 81 to get 81.

$$\frac{81\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{81\times 27}{\left(\frac{1}{3}\right)^{-7}}$$

Multiply 81 and 27 to get 2187.

$$\frac{2187}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate \frac{1}{3} to the power of -7 and get 2187.

$$\frac{2187}{2187}$$

Divide 2187 by 2187 to get 1.

$$1$$

Factor

$$1$$