Solve 45*5^3*2^96/8*5^-5*3^-3

$$\frac { 45 \times 5 ^ { 3 } \times 2 ^ { 96 } } { 8 \times 5 ^ { - 5 } \times 3 ^ { - 3 } }$$

Evaluate

$$4700303586661678231257612288000000000$$

Solution Steps

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

$$\frac{45\times 2^{96}\times 5^{8}}{8\times 3^{-3}}$$

Calculate 2 to the power of 96 and get 79228162514264337593543950336.

$$\frac{45\times 79228162514264337593543950336\times 5^{8}}{8\times 3^{-3}}$$

Multiply 45 and 79228162514264337593543950336 to get 3565267313141895191709477765120.

$$\frac{3565267313141895191709477765120\times 5^{8}}{8\times 3^{-3}}$$

Calculate 5 to the power of 8 and get 390625.

$$\frac{3565267313141895191709477765120\times 390625}{8\times 3^{-3}}$$

Multiply 3565267313141895191709477765120 and 390625 to get 1392682544196052809261514752000000000.

$$\frac{1392682544196052809261514752000000000}{8\times 3^{-3}}$$

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

$$\frac{1392682544196052809261514752000000000}{8\times \frac{1}{27}}$$

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

$$\frac{1392682544196052809261514752000000000}{\frac{8}{27}}$$

Divide 1392682544196052809261514752000000000 by \frac{8}{27} by multiplying 1392682544196052809261514752000000000 by the reciprocal of \frac{8}{27}.

$$1392682544196052809261514752000000000\times \frac{27}{8}$$

Multiply 1392682544196052809261514752000000000 and \frac{27}{8} to get 4700303586661678231257612288000000000.

$$4700303586661678231257612288000000000$$

Factor

$$2^{93}\times 3^{5}\times 5^{9}$$