Solve 5x^7y^2/5xy^2

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

Evaluate

$$x^{6}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 1.

$$5^{0}x^{7-1}y^{2-2}$$

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

$$x^{7-1}y^{2-2}$$

Subtract 1 from 7.

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

Subtract 2 from 2.

$$x^{6}y^{0}$$

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

$$5^{0}x^{6}$$

For any term t except 0, t^{0}=1.

$$1x^{6}$$

For any term t, t\times 1=t and 1t=t.

$$x^{6}$$

Differentiate w.r.t. x

$$6x^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{2}}{5y^{2}}x^{7-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6})$$

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}.

$$6x^{6-1}$$

Do the arithmetic.

$$6x^{5}$$