Solve frac{(3^{-2}*7^{2})^{-5}*(7^{-2}*3^{-3})^-6}{((3^-2)^-4)^2}

$$\frac { ( 3 ^ { - 2 } \cdot 7 ^ { 2 } ) ^ { - 5 } \cdot ( 7 ^ { - 2 } \cdot 3 ^ { - 3 } ) ^ { - 6 } } { ( ( 3 ^ { - 2 } ) ^ { - 4 } ) ^ { 2 } }$$

Evaluate

$$26040609$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and -4 to get 8.

$$\frac{\left(3^{-2}\times 7^{2}\right)^{-5}\times \left(7^{-2}\times 3^{-3}\right)^{-6}}{\left(3^{8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\left(3^{-2}\times 7^{2}\right)^{-5}\times \left(7^{-2}\times 3^{-3}\right)^{-6}}{3^{16}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\left(\frac{1}{9}\times 7^{2}\right)^{-5}\times \left(7^{-2}\times 3^{-3}\right)^{-6}}{3^{16}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\left(\frac{1}{9}\times 49\right)^{-5}\times \left(7^{-2}\times 3^{-3}\right)^{-6}}{3^{16}}$$

Multiply \frac{1}{9} and 49 to get \frac{49}{9}.

$$\frac{\left(\frac{49}{9}\right)^{-5}\times \left(7^{-2}\times 3^{-3}\right)^{-6}}{3^{16}}$$

Calculate \frac{49}{9} to the power of -5 and get \frac{59049}{282475249}.

$$\frac{\frac{59049}{282475249}\times \left(7^{-2}\times 3^{-3}\right)^{-6}}{3^{16}}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{\frac{59049}{282475249}\times \left(\frac{1}{49}\times 3^{-3}\right)^{-6}}{3^{16}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{59049}{282475249}\times \left(\frac{1}{49}\times \frac{1}{27}\right)^{-6}}{3^{16}}$$

Multiply \frac{1}{49} and \frac{1}{27} to get \frac{1}{1323}.

$$\frac{\frac{59049}{282475249}\times \left(\frac{1}{1323}\right)^{-6}}{3^{16}}$$

Calculate \frac{1}{1323} to the power of -6 and get 5362398255800861289.

$$\frac{\frac{59049}{282475249}\times 5362398255800861289}{3^{16}}$$

Multiply \frac{59049}{282475249} and 5362398255800861289 to get 1120962830293089.

$$\frac{1120962830293089}{3^{16}}$$

Calculate 3 to the power of 16 and get 43046721.

$$\frac{1120962830293089}{43046721}$$

Divide 1120962830293089 by 43046721 to get 26040609.

$$26040609$$

Factor

$$3^{12}\times 7^{2}$$