Solve frac{6^{-4}*12^{2}*(5^3)^-2}{(30*5^2)^2}

$$\frac { 6 ^ { - 4 } \times 12 ^ { 2 } \times ( 5 ^ { 3 } ) ^ { - 2 } } { ( 30 \times 5 ^ { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{1}{79101562500}\approx 1.264197531 \cdot 10^{-11}$$

Solution Steps

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

$$\frac{6^{-4}\times 12^{2}\times 5^{-6}}{\left(30\times 5^{2}\right)^{2}}$$

Calculate 6 to the power of -4 and get \frac{1}{1296}.

$$\frac{\frac{1}{1296}\times 12^{2}\times 5^{-6}}{\left(30\times 5^{2}\right)^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{\frac{1}{1296}\times 144\times 5^{-6}}{\left(30\times 5^{2}\right)^{2}}$$

Multiply \frac{1}{1296} and 144 to get \frac{1}{9}.

$$\frac{\frac{1}{9}\times 5^{-6}}{\left(30\times 5^{2}\right)^{2}}$$

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

$$\frac{\frac{1}{9}\times \frac{1}{15625}}{\left(30\times 5^{2}\right)^{2}}$$

Multiply \frac{1}{9} and \frac{1}{15625} to get \frac{1}{140625}.

$$\frac{\frac{1}{140625}}{\left(30\times 5^{2}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{1}{140625}}{\left(30\times 25\right)^{2}}$$

Multiply 30 and 25 to get 750.

$$\frac{\frac{1}{140625}}{750^{2}}$$

Calculate 750 to the power of 2 and get 562500.

$$\frac{\frac{1}{140625}}{562500}$$

Express \frac{\frac{1}{140625}}{562500} as a single fraction.

$$\frac{1}{140625\times 562500}$$

Multiply 140625 and 562500 to get 79101562500.

$$\frac{1}{79101562500}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 ^ {4} \cdot 5 ^ {12}} = 1.2641975308641975 \times 10^{-11}$$