Solve (m^7)^2

$$( m ^ { 7 } ) ^ { 2 }$$

Evaluate

$$m^{14}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(m^{7}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$m^{7\times 2}$$

Multiply 7 times 2.

$$m^{14}$$

Differentiate w.r.t. m

$$14m^{13}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$2\left(m^{7}\right)^{2-1}\frac{\mathrm{d}}{\mathrm{d}m}(m^{7})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\left(m^{7}\right)^{1}\times 7m^{7-1}$$

Simplify.

$$14m^{6}\left(m^{7}\right)^{1}$$

For any term t, t^{1}=t.

$$14m^{6}m^{7}$$