Solve 2x^-2y^-2/16x^-12y^2

$$\frac { 2 x ^ { - 2 } y ^ { - 2 } } { 16 x ^ { - 12 } y ^ { 2 } }$$

Evaluate

$$\frac{x^{10}}{8y^{4}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{x^{-2}y^{-2}}{8x^{-12}y^{2}}$$

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

$$\frac{y^{-2}x^{10}}{8y^{2}}$$

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

$$\frac{x^{10}}{8y^{4}}$$

Differentiate w.r.t. x

$$\frac{5x^{9}}{4y^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{y^{2}\times 16y^{2}}x^{-2-\left(-12\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{8y^{4}}x^{10})$$

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}.

$$10\times \frac{1}{8y^{4}}x^{10-1}$$

Do the arithmetic.

$$\frac{5}{4y^{4}}x^{9}$$