Solve x^-3+(x^2)^4/x^5

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

Evaluate

$$x^{3}+\frac{1}{x^{8}}$$

Short Solution Steps

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

$$\frac{x^{-3}+x^{8}}{x^{5}}$$

Factor the expressions that are not already factored.

$$\frac{x^{-3}\left(x+1\right)\left(x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)}{x^{5}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\left(x+1\right)\left(x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)}{x^{8}}$$

Expand the expression.

$$\frac{x^{11}+1}{x^{8}}$$

Expand

$$x^{3}+\frac{1}{x^{8}}$$

Short Solution Steps

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

$$\frac{x^{-3}+x^{8}}{x^{5}}$$

Factor the expressions that are not already factored.

$$\frac{x^{-3}\left(x+1\right)\left(x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)}{x^{5}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\left(x+1\right)\left(x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)}{x^{8}}$$

Expand the expression.

$$\frac{x^{11}+1}{x^{8}}$$