Solve 2(x^{3})^{2}*x^{3}-(3x^3)^3+(5x)^2*x^7

$$2 ( x ^ { 3 } ) ^ { 2 } \cdot x ^ { 3 } - ( 3 x ^ { 3 } ) ^ { 3 } + ( 5 x ) ^ { 2 } \cdot x ^ { 7 }$$

Evaluate

$$0$$

Solution Steps

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

$$2x^{6}x^{3}-\left(3x^{3}\right)^{3}+\left(5x\right)^{2}x^{7}$$

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

$$2x^{9}-\left(3x^{3}\right)^{3}+\left(5x\right)^{2}x^{7}$$

Expand \left(3x^{3}\right)^{3}.

$$2x^{9}-3^{3}\left(x^{3}\right)^{3}+\left(5x\right)^{2}x^{7}$$

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

$$2x^{9}-3^{3}x^{9}+\left(5x\right)^{2}x^{7}$$

Calculate 3 to the power of 3 and get 27.

$$2x^{9}-27x^{9}+\left(5x\right)^{2}x^{7}$$

Combine 2x^{9} and -27x^{9} to get -25x^{9}.

$$-25x^{9}+\left(5x\right)^{2}x^{7}$$

Expand \left(5x\right)^{2}.

$$-25x^{9}+5^{2}x^{2}x^{7}$$

Calculate 5 to the power of 2 and get 25.

$$-25x^{9}+25x^{2}x^{7}$$

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

$$-25x^{9}+25x^{9}$$

Combine -25x^{9} and 25x^{9} to get 0.

$$0$$

Factor

$$0$$