Solve 7a/12div(2a^2)^3/-6a

$$\frac { 7 a } { 12 } \div \frac { ( 2 a ^ { 2 } ) ^ { 3 } } { - 6 a }$$

Evaluate

$$-\frac{7}{16a^{4}}$$

Solution Steps

Divide \frac{7a}{12} by \frac{\left(2a^{2}\right)^{3}}{-6a} by multiplying \frac{7a}{12} by the reciprocal of \frac{\left(2a^{2}\right)^{3}}{-6a}.

$$\frac{7a\left(-6\right)a}{12\times \left(2a^{2}\right)^{3}}$$

Cancel out 6 in both numerator and denominator.

$$\frac{-7aa}{2\times \left(2a^{2}\right)^{3}}$$

Multiply a and a to get a^{2}.

$$\frac{-7a^{2}}{2\times \left(2a^{2}\right)^{3}}$$

Expand \left(2a^{2}\right)^{3}.

$$\frac{-7a^{2}}{2\times 2^{3}\left(a^{2}\right)^{3}}$$

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

$$\frac{-7a^{2}}{2\times 2^{3}a^{6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-7a^{2}}{2\times 8a^{6}}$$

Multiply 2 and 8 to get 16.

$$\frac{-7a^{2}}{16a^{6}}$$

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

$$\frac{-7}{16a^{4}}$$

Expand

$$-\frac{7}{16a^{4}}$$

Solution Steps

Divide \frac{7a}{12} by \frac{\left(2a^{2}\right)^{3}}{-6a} by multiplying \frac{7a}{12} by the reciprocal of \frac{\left(2a^{2}\right)^{3}}{-6a}.

$$\frac{7a\left(-6\right)a}{12\times \left(2a^{2}\right)^{3}}$$

Cancel out 6 in both numerator and denominator.

$$\frac{-7aa}{2\times \left(2a^{2}\right)^{3}}$$

Multiply a and a to get a^{2}.

$$\frac{-7a^{2}}{2\times \left(2a^{2}\right)^{3}}$$

Expand \left(2a^{2}\right)^{3}.

$$\frac{-7a^{2}}{2\times 2^{3}\left(a^{2}\right)^{3}}$$

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

$$\frac{-7a^{2}}{2\times 2^{3}a^{6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-7a^{2}}{2\times 8a^{6}}$$

Multiply 2 and 8 to get 16.

$$\frac{-7a^{2}}{16a^{6}}$$

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

$$\frac{-7}{16a^{4}}$$