Solve -100a^4t^2ydiv1/4at^2y

$$- 100 a ^ { 4 } t ^ { 2 } y \div \frac { 1 } { 4 } a t ^ { 2 } y$$

Evaluate

$$-400y^{2}t^{4}a^{5}$$

Solution Steps

Divide -100a^{4}t^{2}y by \frac{1}{4} by multiplying -100a^{4}t^{2}y by the reciprocal of \frac{1}{4}.

$$-100a^{4}t^{2}y\times 4at^{2}y$$

Multiply -100 and 4 to get -400.

$$-400a^{4}t^{2}yat^{2}y$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-400a^{5}t^{2}yt^{2}y$$

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

$$-400a^{5}t^{4}yy$$

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

$$-400a^{5}t^{4}y^{2}$$

Differentiate w.r.t. a

$$-2000y^{2}\left(at\right)^{4}$$