Solve 8x^7y^6/8x^5y^2

$$\frac { 8 x ^ { 7 } y ^ { 6 } } { 8 x ^ { 5 } y ^ { 2 } }$$

Evaluate

$$x^{2}y^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}x^{7}y^{6}}{8^{1}x^{5}y^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$8^{1-1}x^{7-5}y^{6-2}$$

Subtract 1 from 1.

$$8^{0}x^{7-5}y^{6-2}$$

For any number a except 0, a^{0}=1.

$$x^{7-5}y^{6-2}$$

Subtract 5 from 7.

$$x^{2}y^{6-2}$$

Subtract 2 from 6.

$$x^{2}y^{4}$$

Differentiate w.r.t. x

$$2xy^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y^{6}}{8y^{2}}x^{7-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y^{4}x^{2})$$

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}.

$$2y^{4}x^{2-1}$$

Do the arithmetic.

$$2y^{4}x^{1}$$

For any term t, t^{1}=t.

$$2y^{4}x$$