Solve frac{[3^{2}*(-3)^3*3*(-3)^2]^2}{[3*(-3)]^4}

$$\frac { [ 3 ^ { 2 } \cdot ( - 3 ) ^ { 3 } \times 3 \times ( - 3 ) ^ { 2 } ] ^ { 2 } } { [ 3 \times ( - 3 ) ] ^ { 4 } }$$

Evaluate

$$6561$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(3^{3}\left(-3\right)^{3}\left(-3\right)^{2}\right)^{2}}{\left(3\left(-3\right)\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\left(3^{3}\left(-3\right)^{5}\right)^{2}}{\left(3\left(-3\right)\right)^{4}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\left(27\left(-3\right)^{5}\right)^{2}}{\left(3\left(-3\right)\right)^{4}}$$

Calculate -3 to the power of 5 and get -243.

$$\frac{\left(27\left(-243\right)\right)^{2}}{\left(3\left(-3\right)\right)^{4}}$$

Multiply 27 and -243 to get -6561.

$$\frac{\left(-6561\right)^{2}}{\left(3\left(-3\right)\right)^{4}}$$

Calculate -6561 to the power of 2 and get 43046721.

$$\frac{43046721}{\left(3\left(-3\right)\right)^{4}}$$

Multiply 3 and -3 to get -9.

$$\frac{43046721}{\left(-9\right)^{4}}$$

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

$$\frac{43046721}{6561}$$

Divide 43046721 by 6561 to get 6561.

$$6561$$

Factor

$$3^{8}$$