Solve x^3div11divx^3div22

$${ x }^{ 3 \div 11 } \div { x }^{ 3 \div 22 }$$

Evaluate

$$x^{\frac{3}{22}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{\frac{3}{11}}}{x^{\frac{3}{22}}}$$

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

$$x^{\frac{3}{11}-\frac{3}{22}}$$

Subtract \frac{3}{22} from \frac{3}{11} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{\frac{3}{22}}$$

Differentiate w.r.t. x

$$\frac{3}{22x^{\frac{19}{22}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{\frac{3}{11}-\frac{3}{22}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{3}{22}})$$

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}.

$$\frac{3}{22}x^{\frac{3}{22}-1}$$

Do the arithmetic.

$$\frac{3}{22}x^{-\frac{19}{22}}$$