Solve frac{25x^{-8}y^9(x)^-2}{5x^-8y^-9}

$$\frac { 25 x ^ { - 8 } y ^ { 9 } ( x ) ^ { - 2 } } { 5 x ^ { - 8 } y ^ { - 9 } }$$

Evaluate

$$\frac{5y^{18}}{x^{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -8 and -2 to get -10.

$$\frac{25x^{-10}y^{9}}{5x^{-8}y^{-9}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{5x^{-10}y^{9}}{y^{-9}x^{-8}}$$

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

$$\frac{5x^{-10}y^{18}}{x^{-8}}$$

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

$$\frac{5y^{18}}{x^{2}}$$

Differentiate w.r.t. x

$$-\frac{10y^{18}}{x^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{25y^{9}}{x^{2}\times \frac{5}{y^{9}}}x^{-8-\left(-8\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{18}}{x^{2}}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{18}}{x^{2}})$$

The derivative of a constant term is 0.

$$0$$