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

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

Evaluate

$$4x^{9}$$

Solution Steps

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

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

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

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

Calculate -3 to the power of 3 and get -27.

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

The opposite of -27x^{9} is 27x^{9}.

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

Combine 2x^{9} and 27x^{9} to get 29x^{9}.

$$29x^{9}-\left(-5x\right)^{2}x^{7}$$

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

$$29x^{9}-\left(-5\right)^{2}x^{2}x^{7}$$

Calculate -5 to the power of 2 and get 25.

$$29x^{9}-25x^{2}x^{7}$$

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

$$29x^{9}-25x^{9}$$

Combine 29x^{9} and -25x^{9} to get 4x^{9}.

$$4x^{9}$$

Expand

$$4x^{9}$$

Solution Steps

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

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

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

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

Calculate -3 to the power of 3 and get -27.

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

The opposite of -27x^{9} is 27x^{9}.

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

Combine 2x^{9} and 27x^{9} to get 29x^{9}.

$$29x^{9}-\left(-5x\right)^{2}x^{7}$$

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

$$29x^{9}-\left(-5\right)^{2}x^{2}x^{7}$$

Calculate -5 to the power of 2 and get 25.

$$29x^{9}-25x^{2}x^{7}$$

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

$$29x^{9}-25x^{9}$$

Combine 29x^{9} and -25x^{9} to get 4x^{9}.

$$4x^{9}$$