Solve 27x^6y^-4/-3x^-3y

$$\frac { 27 x ^ { 6 } y ^ { - 4 } } { - 3 x ^ { - 3 } y }$$

Evaluate

$$-\frac{9x^{9}}{y^{5}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{9y^{-4}x^{6}}{-x^{-3}y}$$

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

$$\frac{9y^{-4}x^{9}}{-y}$$

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

$$\frac{9x^{9}}{-y^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-9x^{9}}{y^{5}}$$

Differentiate w.r.t. x

$$-\frac{81x^{8}}{y^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{27}{y^{4}\left(-3y\right)}x^{6-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{9}{y^{5}}\right)x^{9})$$

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}.

$$9\left(-\frac{9}{y^{5}}\right)x^{9-1}$$

Do the arithmetic.

$$\left(-\frac{81}{y^{5}}\right)x^{8}$$