Solve (x^3)^5div(x^3)^2

$$( x ^ { 3 } ) ^ { 5 } \div ( x ^ { 3 } ) ^ { 2 }$$

Evaluate

$$x^{9}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{x^{15}}{\left(x^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{x^{15}}{x^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 15 to get 9.

$$x^{9}$$

Differentiate w.r.t. x

$$9x^{8}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{15}}{\left(x^{3}\right)^{2}})$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{15}}{x^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 15 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{9})$$

The derivative of ax^{n} is nax^{n-1}.

$$9x^{9-1}$$

Subtract 1 from 9.

$$9x^{8}$$