Solve h^5*h^3*h^7

$$h ^ { 5 } \times h ^ { 3 } \times h ^ { 7 }$$

Evaluate

$$h^{15}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$h^{5}h^{3}h^{7}$$

Use the Multiplication Rule for Exponents.

$$h^{5+3+7}$$

Add the exponents 5 and 3.

$$h^{8+7}$$

Add the exponents 8 and 7.

$$h^{15}$$

Differentiate w.r.t. h

$$15h^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}h}(h^{8}h^{7})$$

To multiply powers of the same base, add their exponents. Add 8 and 7 to get 15.

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

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

$$15h^{15-1}$$

Subtract 1 from 15.

$$15h^{14}$$