Solve [3^{12}*(-9^{5})*(27)^2]^2:(5^3)^9

$$[ 3 ^ { 12 } \cdot ( - 9 ^ { 5 } ) \cdot ( 27 ) ^ { 2 } ] ^ { 2 } : ( 5 ^ { 3 } ) ^ { 9 }$$

Evaluate

$$\frac{523347633027360537213511521}{7450580596923828125}\approx 70242530.259110093$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 9 to get 27.

$$\frac{\left(3^{12}\left(-9^{5}\right)\times 27^{2}\right)^{2}}{5^{27}}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{\left(531441\left(-9^{5}\right)\times 27^{2}\right)^{2}}{5^{27}}$$

Calculate 9 to the power of 5 and get 59049.

$$\frac{\left(531441\left(-59049\right)\times 27^{2}\right)^{2}}{5^{27}}$$

Multiply 531441 and -59049 to get -31381059609.

$$\frac{\left(-31381059609\times 27^{2}\right)^{2}}{5^{27}}$$

Calculate 27 to the power of 2 and get 729.

$$\frac{\left(-31381059609\times 729\right)^{2}}{5^{27}}$$

Multiply -31381059609 and 729 to get -22876792454961.

$$\frac{\left(-22876792454961\right)^{2}}{5^{27}}$$

Calculate -22876792454961 to the power of 2 and get 523347633027360537213511521.

$$\frac{523347633027360537213511521}{5^{27}}$$

Calculate 5 to the power of 27 and get 7450580596923828125.

$$\frac{523347633027360537213511521}{7450580596923828125}$$

Factor

$$\frac{3 ^ {56}}{5 ^ {27}} = 70242530\frac{1.9305206552435712 \times 10^{18}}{7.450580596923828 \times 10^{18}} = 70242530.2591101$$