Solve 45*5^3*2^9/8*5^-5*3^-3

$$\frac { 45 \times 5 ^ { 3 } \times 2 ^ { 9 } } { 8 \times 5 ^ { - 5 } \times 3 ^ { - 3 } }$$

Evaluate

$$30375000000$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{45\times 2^{9}\times 5^{8}}{8\times 3^{-3}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{45\times 512\times 5^{8}}{8\times 3^{-3}}$$

Multiply 45 and 512 to get 23040.

$$\frac{23040\times 5^{8}}{8\times 3^{-3}}$$

Calculate 5 to the power of 8 and get 390625.

$$\frac{23040\times 390625}{8\times 3^{-3}}$$

Multiply 23040 and 390625 to get 9000000000.

$$\frac{9000000000}{8\times 3^{-3}}$$

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

$$\frac{9000000000}{8\times \frac{1}{27}}$$

Multiply 8 and \frac{1}{27} to get \frac{8}{27}.

$$\frac{9000000000}{\frac{8}{27}}$$

Divide 9000000000 by \frac{8}{27} by multiplying 9000000000 by the reciprocal of \frac{8}{27}.

$$9000000000\times \frac{27}{8}$$

Multiply 9000000000 and \frac{27}{8} to get 30375000000.

$$30375000000$$

Factor

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