Solve 5(x^{3})^{2}*x^{6}-(3x^4)^3+(2x)^3x^4

$$5 ( x ^ { 3 } ) ^ { 2 } \cdot x ^ { 6 } - ( 3 x ^ { 4 } ) ^ { 3 } + ( 2 x ) ^ { 3 } x ^ { 4 }$$

Evaluate

$$8x^{7}-22x^{12}$$

Solution Steps

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

$$5x^{6}x^{6}-\left(3x^{4}\right)^{3}+\left(2x\right)^{3}x^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$5x^{12}-\left(3x^{4}\right)^{3}+\left(2x\right)^{3}x^{4}$$

Expand \left(3x^{4}\right)^{3}.

$$5x^{12}-3^{3}\left(x^{4}\right)^{3}+\left(2x\right)^{3}x^{4}$$

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

$$5x^{12}-3^{3}x^{12}+\left(2x\right)^{3}x^{4}$$

Calculate 3 to the power of 3 and get 27.

$$5x^{12}-27x^{12}+\left(2x\right)^{3}x^{4}$$

Combine 5x^{12} and -27x^{12} to get -22x^{12}.

$$-22x^{12}+\left(2x\right)^{3}x^{4}$$

Expand \left(2x\right)^{3}.

$$-22x^{12}+2^{3}x^{3}x^{4}$$

Calculate 2 to the power of 3 and get 8.

$$-22x^{12}+8x^{3}x^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-22x^{12}+8x^{7}$$

Expand

$$8x^{7}-22x^{12}$$

Solution Steps

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

$$5x^{6}x^{6}-\left(3x^{4}\right)^{3}+\left(2x\right)^{3}x^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$5x^{12}-\left(3x^{4}\right)^{3}+\left(2x\right)^{3}x^{4}$$

Expand \left(3x^{4}\right)^{3}.

$$5x^{12}-3^{3}\left(x^{4}\right)^{3}+\left(2x\right)^{3}x^{4}$$

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

$$5x^{12}-3^{3}x^{12}+\left(2x\right)^{3}x^{4}$$

Calculate 3 to the power of 3 and get 27.

$$5x^{12}-27x^{12}+\left(2x\right)^{3}x^{4}$$

Combine 5x^{12} and -27x^{12} to get -22x^{12}.

$$-22x^{12}+\left(2x\right)^{3}x^{4}$$

Expand \left(2x\right)^{3}.

$$-22x^{12}+2^{3}x^{3}x^{4}$$

Calculate 2 to the power of 3 and get 8.

$$-22x^{12}+8x^{3}x^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-22x^{12}+8x^{7}$$