Solve frac{a^{2}+3a^2*2a^4}{(7a^4)^2}

$$\frac { a ^ { 2 } + 3 a ^ { 2 } \times 2 a ^ { 4 } } { ( 7 a ^ { 4 } ) ^ { 2 } }$$

Evaluate

$$\frac{6}{49a^{2}}+\frac{1}{49a^{6}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{a^{2}+3a^{6}\times 2}{\left(7a^{4}\right)^{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{a^{2}+6a^{6}}{\left(7a^{4}\right)^{2}}$$

Expand \left(7a^{4}\right)^{2}.

$$\frac{a^{2}+6a^{6}}{7^{2}\left(a^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{a^{2}+6a^{6}}{7^{2}a^{8}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{a^{2}+6a^{6}}{49a^{8}}$$

Factor the expressions that are not already factored.

$$\frac{a^{2}\left(6a^{4}+1\right)}{49a^{8}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{6a^{4}+1}{49a^{6}}$$

Expand

$$\frac{6}{49a^{2}}+\frac{1}{49a^{6}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{a^{2}+3a^{6}\times 2}{\left(7a^{4}\right)^{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{a^{2}+6a^{6}}{\left(7a^{4}\right)^{2}}$$

Expand \left(7a^{4}\right)^{2}.

$$\frac{a^{2}+6a^{6}}{7^{2}\left(a^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{a^{2}+6a^{6}}{7^{2}a^{8}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{a^{2}+6a^{6}}{49a^{8}}$$

Factor the expressions that are not already factored.

$$\frac{a^{2}\left(6a^{4}+1\right)}{49a^{8}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{6a^{4}+1}{49a^{6}}$$