Solve frac{2^{3}*3^{2}}{5^-1}div2^2*3/5^-2]*5^2/2*3=

$$\frac { 2 ^ { 3 } \cdot 3 ^ { 2 } } { 5 ^ { - 1 } } \div \frac { 2 ^ { 2 } \cdot 3 } { 5 ^ { - 2 } } ] \cdot \frac { 5 ^ { 2 } } { 2 \cdot 3 } =$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Divide \frac{2^{3}\times 3^{2}}{5^{-1}} by \frac{2^{2}\times 3}{5^{-2}} by multiplying \frac{2^{3}\times 3^{2}}{5^{-1}} by the reciprocal of \frac{2^{2}\times 3}{5^{-2}}.

$$\frac{2^{3}\times 3^{2}\times 5^{-2}}{5^{-1}\times 2^{2}\times 3}$$

Cancel out 3\times 2^{2} in both numerator and denominator.

$$\frac{2\times 3\times 5^{-2}}{\frac{1}{5}}$$

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

$$\frac{2\times 3}{5^{1}}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5^{1}}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$