Solve -49x^2y^4/56x^5y^5=

$$\frac { - 49 x ^ { 2 } y ^ { 4 } } { 56 x ^ { 5 } y ^ { 5 } } =$$

Evaluate

$$-\frac{7}{8yx^{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-49\right)^{1}x^{2}y^{4}}{56^{1}x^{5}y^{5}}$$

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

$$\frac{\left(-49\right)^{1}}{56^{1}}x^{2-5}y^{4-5}$$

Subtract 5 from 2.

$$\frac{\left(-49\right)^{1}}{56^{1}}x^{-3}y^{4-5}$$

Subtract 5 from 4.

$$\frac{\left(-49\right)^{1}}{56^{1}}\times \frac{1}{x^{3}}\times \frac{1}{y}$$

Reduce the fraction \frac{-49}{56} to lowest terms by extracting and canceling out 7.

$$-\frac{7}{8}\times \frac{1}{x^{3}}\times \frac{1}{y}$$

Differentiate w.r.t. x

$$\frac{21}{8yx^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{49y^{4}}{56y^{5}}\right)x^{2-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{7}{8y}\right)x^{-3})$$

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}.

$$-3\left(-\frac{7}{8y}\right)x^{-3-1}$$

Do the arithmetic.

$$\frac{21}{8y}x^{-4}$$