Solve 6x^-2-1/(2x^3)^2

$$6 x ^ { - 2 } - \frac { 1 } { ( 2 x ^ { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{6}{x^{2}}-\frac{1}{4x^{6}}$$

Short Solution Steps

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

$$6x^{-2}-\frac{1}{2^{2}\left(x^{3}\right)^{2}}$$

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

$$6x^{-2}-\frac{1}{2^{2}x^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$6x^{-2}-\frac{1}{4x^{6}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{-2} times \frac{4x^{6}}{4x^{6}}.

$$\frac{6x^{-2}\times 4x^{6}}{4x^{6}}-\frac{1}{4x^{6}}$$

Since \frac{6x^{-2}\times 4x^{6}}{4x^{6}} and \frac{1}{4x^{6}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x^{-2}\times 4x^{6}-1}{4x^{6}}$$

Do the multiplications in 6x^{-2}\times 4x^{6}-1.

$$\frac{24x^{4}-1}{4x^{6}}$$

Expand

$$\frac{6}{x^{2}}-\frac{1}{4x^{6}}$$

Short Solution Steps

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

$$6x^{-2}-\frac{1}{2^{2}\left(x^{3}\right)^{2}}$$

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

$$6x^{-2}-\frac{1}{2^{2}x^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$6x^{-2}-\frac{1}{4x^{6}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{-2} times \frac{4x^{6}}{4x^{6}}.

$$\frac{6x^{-2}\times 4x^{6}}{4x^{6}}-\frac{1}{4x^{6}}$$

Since \frac{6x^{-2}\times 4x^{6}}{4x^{6}} and \frac{1}{4x^{6}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x^{-2}\times 4x^{6}-1}{4x^{6}}$$

Do the multiplications in 6x^{-2}\times 4x^{6}-1.

$$\frac{24x^{4}-1}{4x^{6}}$$