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

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

Evaluate

$$x^{6}\left(1+x-2x^{7}\right)$$

Solution Steps

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

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

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

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

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

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

Calculate -x^{5} to the power of 2 and get \left(x^{5}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$x^{7}-2x^{3}x^{10}+x^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$x^{7}-2x^{13}+x^{6}$$

Expand

$$x^{6}+x^{7}-2x^{13}$$

Solution Steps

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.

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

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

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

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

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

Calculate -x^{5} to the power of 2 and get \left(x^{5}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$x^{7}-2x^{3}x^{10}+x^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$x^{7}-2x^{13}+x^{6}$$