Solve frac{7^{-3}*7^-1*7^4}{(7^5*7)^2}=

$$\frac { 7 ^ { - 3 } \cdot 7 ^ { - 1 } \cdot 7 ^ { 4 } } { ( 7 ^ { 5 } \cdot 7 ) ^ { 2 } } =$$

Evaluate

$$\frac{1}{13841287201}\approx 7.224761581 \cdot 10^{-11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -1 to get -4.

$$\frac{7^{-4}\times 7^{4}}{\left(7^{5}\times 7\right)^{2}}$$

Multiply 7^{-4} and 7^{4} to get 1.

$$\frac{1}{\left(7^{5}\times 7\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{1}{\left(7^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{1}{7^{12}}$$

Calculate 7 to the power of 12 and get 13841287201.

$$\frac{1}{13841287201}$$

Factor

$$\frac{1}{7 ^ {12}} = 7.224761580900889 \times 10^{-11}$$