Solve (h^5)^3/h^6=

$$\frac { ( h ^ { 5 } ) ^ { 3 } } { h ^ { 6 } } =$$

Evaluate

$$h^{9}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(h^{5}\right)^{3}\times \frac{1}{h^{6}}$$

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

$$h^{5\times 3}h^{6\left(-1\right)}$$

Multiply 5 times 3.

$$h^{15}h^{6\left(-1\right)}$$

Multiply 6 times -1.

$$h^{15}h^{-6}$$

To multiply powers of the same base, add their exponents.

$$h^{15-6}$$

Add the exponents 15 and -6.

$$h^{9}$$

Differentiate w.r.t. h

$$9h^{8}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{h^{15}}{h^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 15 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}h}(h^{9})$$

The derivative of ax^{n} is nax^{n-1}.

$$9h^{9-1}$$

Subtract 1 from 9.

$$9h^{8}$$