Solve 5y^10*5y^-3

$$5 y ^ { 10 } \times 5 y ^ { - 3 }$$

Evaluate

$$25y^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and -3 to get 7.

$$5y^{7}\times 5$$

Multiply 5 and 5 to get 25.

$$25y^{7}$$

Differentiate w.r.t. y

$$175y^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and -3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{7}\times 5)$$

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}y}(25y^{7})$$

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

$$7\times 25y^{7-1}$$

Multiply 7 times 25.

$$175y^{7-1}$$

Subtract 1 from 7.

$$175y^{6}$$