Solve 4(x^{3})^{2}*x^3-(3x^3)^3+(6x)^2*x

$$4 ( x ^ { 3 } ) ^ { 2 } \cdot x ^ { 3 } - ( 3 x ^ { 3 } ) ^ { 3 } + ( 6 x ) ^ { 2 } \cdot x$$

Evaluate

$$x^{3}\left(36-23x^{6}\right)$$

Solution Steps

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

$$4x^{6}x^{3}-\left(3x^{3}\right)^{3}+\left(6x\right)^{2}x$$

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

$$4x^{9}-\left(3x^{3}\right)^{3}+\left(6x\right)^{2}x$$

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

$$4x^{9}-3^{3}\left(x^{3}\right)^{3}+\left(6x\right)^{2}x$$

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

$$4x^{9}-3^{3}x^{9}+\left(6x\right)^{2}x$$

Calculate 3 to the power of 3 and get 27.

$$4x^{9}-27x^{9}+\left(6x\right)^{2}x$$

Combine 4x^{9} and -27x^{9} to get -23x^{9}.

$$-23x^{9}+\left(6x\right)^{2}x$$

Expand \left(6x\right)^{2}.

$$-23x^{9}+6^{2}x^{2}x$$

Calculate 6 to the power of 2 and get 36.

$$-23x^{9}+36x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-23x^{9}+36x^{3}$$

Expand

$$36x^{3}-23x^{9}$$

Solution Steps

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

$$4x^{6}x^{3}-\left(3x^{3}\right)^{3}+\left(6x\right)^{2}x$$

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

$$4x^{9}-\left(3x^{3}\right)^{3}+\left(6x\right)^{2}x$$

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

$$4x^{9}-3^{3}\left(x^{3}\right)^{3}+\left(6x\right)^{2}x$$

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

$$4x^{9}-3^{3}x^{9}+\left(6x\right)^{2}x$$

Calculate 3 to the power of 3 and get 27.

$$4x^{9}-27x^{9}+\left(6x\right)^{2}x$$

Combine 4x^{9} and -27x^{9} to get -23x^{9}.

$$-23x^{9}+\left(6x\right)^{2}x$$

Expand \left(6x\right)^{2}.

$$-23x^{9}+6^{2}x^{2}x$$

Calculate 6 to the power of 2 and get 36.

$$-23x^{9}+36x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-23x^{9}+36x^{3}$$