Solve (x^{2})^{3}*x^{3}-(x^{3})^3+(-x)^2*x^9divx^2

$$( x ^ { 2 } ) ^ { 3 } \cdot x ^ { 3 } - ( x ^ { 3 } ) ^ { 3 } + ( - x ) ^ { 2 } \cdot x ^ { 9 } \div x ^ { 2 }$$

Evaluate

$$x^{9}$$

Solution Steps

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

$$x^{6}x^{3}-\left(x^{3}\right)^{3}+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$x^{9}-\left(x^{3}\right)^{3}+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$x^{9}-x^{9}+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

Combine x^{9} and -x^{9} to get 0.

$$0+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$0+\left(-x\right)^{2}x^{7}$$

Anything plus zero gives itself.

$$\left(-x\right)^{2}x^{7}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}x^{7}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$x^{9}$$

Expand

$$x^{9}$$

Solution Steps

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

$$x^{6}x^{3}-\left(x^{3}\right)^{3}+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$x^{9}-\left(x^{3}\right)^{3}+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$x^{9}-x^{9}+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

Combine x^{9} and -x^{9} to get 0.

$$0+\frac{\left(-x\right)^{2}x^{9}}{x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$0+\left(-x\right)^{2}x^{7}$$

Anything plus zero gives itself.

$$\left(-x\right)^{2}x^{7}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}x^{7}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$x^{9}$$