Solve x^{5}*x^{3}-(2x^4)^2+x^10divx^2

$$x ^ { 5 } \cdot x ^ { 3 } - ( 2 x ^ { 4 } ) ^ { 2 } + x ^ { 10 } \div x ^ { 2 }$$

Evaluate

$$-2x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$x^{8}-\left(2x^{4}\right)^{2}+\frac{x^{10}}{x^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$x^{8}-\left(2x^{4}\right)^{2}+x^{8}$$

Expand \left(2x^{4}\right)^{2}.

$$x^{8}-2^{2}\left(x^{4}\right)^{2}+x^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}-2^{2}x^{8}+x^{8}$$

Calculate 2 to the power of 2 and get 4.

$$x^{8}-4x^{8}+x^{8}$$

Combine x^{8} and -4x^{8} to get -3x^{8}.

$$-3x^{8}+x^{8}$$

Combine -3x^{8} and x^{8} to get -2x^{8}.

$$-2x^{8}$$

Expand

$$-2x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$x^{8}-\left(2x^{4}\right)^{2}+\frac{x^{10}}{x^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$x^{8}-\left(2x^{4}\right)^{2}+x^{8}$$

Expand \left(2x^{4}\right)^{2}.

$$x^{8}-2^{2}\left(x^{4}\right)^{2}+x^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}-2^{2}x^{8}+x^{8}$$

Calculate 2 to the power of 2 and get 4.

$$x^{8}-4x^{8}+x^{8}$$

Combine x^{8} and -4x^{8} to get -3x^{8}.

$$-3x^{8}+x^{8}$$

Combine -3x^{8} and x^{8} to get -2x^{8}.

$$-2x^{8}$$