Solve (x^6)^3/(x^3)^4

$$\frac { ( x ^ { 6 } ) ^ { 3 } } { ( x ^ { 3 } ) ^ { 4 } }$$

Evaluate

$$x^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{x^{18}}{\left(x^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{x^{18}}{x^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 18 to get 6.

$$x^{6}$$

Differentiate w.r.t. x

$$6x^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{18}}{\left(x^{3}\right)^{4}})$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{18}}{x^{12}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 18 to get 6.

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

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

$$6x^{6-1}$$

Subtract 1 from 6.

$$6x^{5}$$