Solve (b^9)^8

$$( b ^ { 9 } ) ^ { 8 }$$

Evaluate

$$b^{72}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(b^{9}\right)^{8}$$

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

$$b^{9\times 8}$$

Multiply 9 times 8.

$$b^{72}$$

Differentiate w.r.t. b

$$72b^{71}$$

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).

$$8\left(b^{9}\right)^{8-1}\frac{\mathrm{d}}{\mathrm{d}b}(b^{9})$$

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}.

$$8\left(b^{9}\right)^{7}\times 9b^{9-1}$$

Simplify.

$$72b^{8}\left(b^{9}\right)^{7}$$