Solve frac{(5-3)^{2}*3^9}{(3-2)^-3*(5^3)^-2}

$$\frac { ( 5 - 3 ) ^ { 2 } \times 3 ^ { 9 } } { ( 3 - 2 ) ^ { - 3 } \times ( 5 ^ { 3 } ) ^ { - 2 } }$$

Evaluate

$$1230187500$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

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

Subtract 3 from 5 to get 2.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4\times 3^{9}}{\left(3-2\right)^{-3}\times 5^{-6}}$$

Calculate 3 to the power of 9 and get 19683.

$$\frac{4\times 19683}{\left(3-2\right)^{-3}\times 5^{-6}}$$

Multiply 4 and 19683 to get 78732.

$$\frac{78732}{\left(3-2\right)^{-3}\times 5^{-6}}$$

Subtract 2 from 3 to get 1.

$$\frac{78732}{1^{-3}\times 5^{-6}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{78732}{1\times 5^{-6}}$$

Calculate 5 to the power of -6 and get \frac{1}{15625}.

$$\frac{78732}{1\times \frac{1}{15625}}$$

Multiply 1 and \frac{1}{15625} to get \frac{1}{15625}.

$$\frac{78732}{\frac{1}{15625}}$$

Divide 78732 by \frac{1}{15625} by multiplying 78732 by the reciprocal of \frac{1}{15625}.

$$78732\times 15625$$

Multiply 78732 and 15625 to get 1230187500.

$$1230187500$$

Factor

$$2^{2}\times 3^{9}\times 5^{6}$$