Solve (170/3yd)(170/3yd)(1/6yd)

$$( \frac { 170 } { 3 } y d ) ( \frac { 170 } { 3 } y d ) ( \frac { 1 } { 6 } y d )$$

Evaluate

$$\frac{14450\left(dy\right)^{3}}{27}$$

Solution Steps

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

$$\frac{170}{3}y^{2}d\times \frac{170}{3}d\times \frac{1}{6}yd$$

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

$$\frac{170}{3}y^{3}d\times \frac{170}{3}d\times \frac{1}{6}d$$

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

$$\frac{170}{3}y^{3}d^{2}\times \frac{170}{3}\times \frac{1}{6}d$$

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

$$\frac{170}{3}y^{3}d^{3}\times \frac{170}{3}\times \frac{1}{6}$$

Multiply \frac{170}{3} times \frac{170}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{170\times 170}{3\times 3}y^{3}d^{3}\times \frac{1}{6}$$

Do the multiplications in the fraction \frac{170\times 170}{3\times 3}.

$$\frac{28900}{9}y^{3}d^{3}\times \frac{1}{6}$$

Multiply \frac{28900}{9} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28900\times 1}{9\times 6}y^{3}d^{3}$$

Do the multiplications in the fraction \frac{28900\times 1}{9\times 6}.

$$\frac{28900}{54}y^{3}d^{3}$$

Reduce the fraction \frac{28900}{54} to lowest terms by extracting and canceling out 2.

$$\frac{14450}{27}y^{3}d^{3}$$

Differentiate w.r.t. y

$$\frac{14450y^{2}d^{3}}{9}$$