Solve (-5)*(-5)*(-5)*(-5)*y*y*y*y*y

$$( - 5 ) \cdot ( - 5 ) \cdot ( - 5 ) \cdot ( - 5 ) \cdot y \cdot y \cdot y \cdot y \cdot y$$

Evaluate

$$625y^{5}$$

Solution Steps

Multiply y and y to get y^{2}.

$$-5\left(-5\right)\left(-5\right)\left(-5\right)y^{2}yyy$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-5\left(-5\right)\left(-5\right)\left(-5\right)y^{3}yy$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-5\left(-5\right)\left(-5\right)\left(-5\right)y^{4}y$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-5\left(-5\right)\left(-5\right)\left(-5\right)y^{5}$$

Multiply -5 and -5 to get 25.

$$25\left(-5\right)\left(-5\right)y^{5}$$

Multiply 25 and -5 to get -125.

$$-125\left(-5\right)y^{5}$$

Multiply -125 and -5 to get 625.

$$625y^{5}$$

Differentiate w.r.t. y

$$3125y^{4}$$

Steps Using Definition of a Derivative

Multiply y and y to get y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-5\left(-5\right)\left(-5\right)\left(-5\right)y^{2}yyy)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-5\left(-5\right)\left(-5\right)\left(-5\right)y^{3}yy)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-5\left(-5\right)\left(-5\right)\left(-5\right)y^{4}y)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-5\left(-5\right)\left(-5\right)\left(-5\right)y^{5})$$

Multiply -5 and -5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}y}(25\left(-5\right)\left(-5\right)y^{5})$$

Multiply 25 and -5 to get -125.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-125\left(-5\right)y^{5})$$

Multiply -125 and -5 to get 625.

$$\frac{\mathrm{d}}{\mathrm{d}y}(625y^{5})$$

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

$$5\times 625y^{5-1}$$

Multiply 5 times 625.

$$3125y^{5-1}$$

Subtract 1 from 5.

$$3125y^{4}$$