Solve frac{x^{2}*x^2}{(x^4)^2}+3x^0

$$\frac { x ^ { 2 } \times x ^ { 2 } } { ( x ^ { 4 } ) ^ { 2 } } + 3 x ^ { 0 }$$

Evaluate

$$3+\frac{1}{x^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{x^{4}}{\left(x^{4}\right)^{2}}+3x^{0}$$

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

$$\frac{x^{4}}{x^{8}}+3x^{0}$$

Rewrite x^{8} as x^{4}x^{4}. Cancel out x^{4} in both numerator and denominator.

$$\frac{1}{x^{4}}+3x^{0}$$

Calculate x to the power of 0 and get 1.

$$\frac{1}{x^{4}}+3\times 1$$

Multiply 3 and 1 to get 3.

$$\frac{1}{x^{4}}+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x^{4}}{x^{4}}.

$$\frac{1}{x^{4}}+\frac{3x^{4}}{x^{4}}$$

Since \frac{1}{x^{4}} and \frac{3x^{4}}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{1+3x^{4}}{x^{4}}$$

Factor

$$\frac{3x^{4}+1}{x^{4}}$$