Solve 9/4^6+8^3*32/3^-5+9^-3

$$\frac { 9 } { 4 ^ { 6 } + 8 ^ { 3 } } \times \frac { 32 } { 3 ^ { - 5 } + 9 ^ { - 3 } }$$

Evaluate

$$\frac{729}{64}=11.390625$$

Solution Steps

Calculate 4 to the power of 6 and get 4096.

$$\frac{9}{4096+8^{3}}\times \frac{32}{3^{-5}+9^{-3}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{9}{4096+512}\times \frac{32}{3^{-5}+9^{-3}}$$

Add 4096 and 512 to get 4608.

$$\frac{9}{4608}\times \frac{32}{3^{-5}+9^{-3}}$$

Reduce the fraction \frac{9}{4608} to lowest terms by extracting and canceling out 9.

$$\frac{1}{512}\times \frac{32}{3^{-5}+9^{-3}}$$

Calculate 3 to the power of -5 and get \frac{1}{243}.

$$\frac{1}{512}\times \frac{32}{\frac{1}{243}+9^{-3}}$$

Calculate 9 to the power of -3 and get \frac{1}{729}.

$$\frac{1}{512}\times \frac{32}{\frac{1}{243}+\frac{1}{729}}$$

Add \frac{1}{243} and \frac{1}{729} to get \frac{4}{729}.

$$\frac{1}{512}\times \frac{32}{\frac{4}{729}}$$

Divide 32 by \frac{4}{729} by multiplying 32 by the reciprocal of \frac{4}{729}.

$$\frac{1}{512}\times 32\times \frac{729}{4}$$

Multiply 32 and \frac{729}{4} to get 5832.

$$\frac{1}{512}\times 5832$$

Multiply \frac{1}{512} and 5832 to get \frac{729}{64}.

$$\frac{729}{64}$$

Factor

$$\frac{3 ^ {6}}{2 ^ {6}} = 11\frac{25}{64} = 11.390625$$