Solve frac{a^{2}}{bc^2}div(bc/a^2*b^2c/a^2)

$$\frac { a ^ { 2 } } { b c ^ { 2 } } \div ( \frac { b c } { a ^ { 2 } } \times \frac { b ^ { 2 } c } { a ^ { 2 } } )$$

Evaluate

$$\frac{a^{6}}{\left(bc\right)^{4}}$$

Short Solution Steps

Multiply \frac{bc}{a^{2}} times \frac{b^{2}c}{a^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{a^{2}}{bc^{2}}}{\frac{bcb^{2}c}{a^{2}a^{2}}}$$

Divide \frac{a^{2}}{bc^{2}} by \frac{bcb^{2}c}{a^{2}a^{2}} by multiplying \frac{a^{2}}{bc^{2}} by the reciprocal of \frac{bcb^{2}c}{a^{2}a^{2}}.

$$\frac{a^{2}a^{2}a^{2}}{bc^{2}bcb^{2}c}$$

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

$$\frac{a^{4}a^{2}}{bc^{2}bcb^{2}c}$$

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

$$\frac{a^{6}}{bc^{2}bcb^{2}c}$$

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

$$\frac{a^{6}}{b^{2}c^{2}cb^{2}c}$$

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

$$\frac{a^{6}}{b^{4}c^{2}cc}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{a^{6}}{b^{4}c^{3}c}$$

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

$$\frac{a^{6}}{b^{4}c^{4}}$$

Differentiate w.r.t. a

$$\frac{6a^{5}}{\left(bc\right)^{4}}$$