Solve frac{(3y^{3})(2y^{2})^{2}}{(y^4)^3}*(5y^3)^0

$$\frac { ( 3 y ^ { 3 } ) ( 2 y ^ { 2 } ) ^ { 2 } } { ( y ^ { 4 } ) ^ { 3 } } \cdot ( 5 y ^ { 3 } ) ^ { 0 }$$

Evaluate

$$\frac{12}{y^{5}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{3y^{3}\times \left(2y^{2}\right)^{2}}{y^{12}}\times \left(5y^{3}\right)^{0}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{3\times \left(2y^{2}\right)^{2}}{y^{9}}\times \left(5y^{3}\right)^{0}$$

Expand \left(2y^{2}\right)^{2}.

$$\frac{3\times 2^{2}\left(y^{2}\right)^{2}}{y^{9}}\times \left(5y^{3}\right)^{0}$$

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

$$\frac{3\times 2^{2}y^{4}}{y^{9}}\times \left(5y^{3}\right)^{0}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3\times 4y^{4}}{y^{9}}\times \left(5y^{3}\right)^{0}$$

Multiply 3 and 4 to get 12.

$$\frac{12y^{4}}{y^{9}}\times \left(5y^{3}\right)^{0}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{12}{y^{5}}\times \left(5y^{3}\right)^{0}$$

Calculate 5y^{3} to the power of 0 and get 1.

$$\frac{12}{y^{5}}\times 1$$

Express \frac{12}{y^{5}}\times 1 as a single fraction.

$$\frac{12}{y^{5}}$$

Differentiate w.r.t. y

$$-\frac{60}{y^{6}}$$