Solve (y^{4})^3(y^2q)(q^2)^2

$$( y ^ { 4 } ) ^ { 3 } ( y ^ { 2 } q ) ( q ^ { 2 } ) ^ { 2 }$$

Evaluate

$$q^{5}y^{14}$$

Solution Steps

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

$$y^{12}y^{2}q\left(q^{2}\right)^{2}$$

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

$$y^{12}y^{2}qq^{4}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$y^{14}qq^{4}$$

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

$$y^{14}q^{5}$$

Differentiate w.r.t. y

$$14q^{5}y^{13}$$