Solve (-3x)^-3/x^-2x-9x^-5

$$\frac { ( - 3 x ) ^ { - 3 } } { x ^ { - 2 } x } - 9 x ^ { - 5 }$$

Evaluate

$$-\frac{1}{27x^{2}}-\frac{9}{x^{5}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 1 to get -1.

$$\frac{\left(-3x\right)^{-3}}{x^{-1}}-9x^{-5}$$

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

$$\frac{\left(-3\right)^{-3}x^{-3}}{x^{-1}}-9x^{-5}$$

Calculate -3 to the power of -3 and get -\frac{1}{27}.

$$\frac{-\frac{1}{27}x^{-3}}{x^{-1}}-9x^{-5}$$

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

$$\frac{-\frac{1}{27}}{x^{2}}-9x^{-5}$$

Express \frac{-\frac{1}{27}}{x^{2}} as a single fraction.

$$\frac{-1}{27x^{2}}-9x^{-5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -9x^{-5} times \frac{27x^{2}}{27x^{2}}.

$$\frac{-1}{27x^{2}}+\frac{-9x^{-5}\times 27x^{2}}{27x^{2}}$$

Since \frac{-1}{27x^{2}} and \frac{-9x^{-5}\times 27x^{2}}{27x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-1-9x^{-5}\times 27x^{2}}{27x^{2}}$$

Do the multiplications in -1-9x^{-5}\times 27x^{2}.

$$\frac{-1-243x^{-3}}{27x^{2}}$$

Factor the expressions that are not already factored in \frac{-1-243x^{-3}}{27x^{2}}.

$$\frac{-x^{-3}\left(x^{3}+243\right)}{27x^{2}}$$

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

$$\frac{-\left(x^{3}+243\right)}{27x^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{x^{3}+243}{-27x^{5}}$$

Expand

$$-\frac{1}{27x^{2}}-\frac{9}{x^{5}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 1 to get -1.

$$\frac{\left(-3x\right)^{-3}}{x^{-1}}-9x^{-5}$$

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

$$\frac{\left(-3\right)^{-3}x^{-3}}{x^{-1}}-9x^{-5}$$

Calculate -3 to the power of -3 and get -\frac{1}{27}.

$$\frac{-\frac{1}{27}x^{-3}}{x^{-1}}-9x^{-5}$$

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

$$\frac{-\frac{1}{27}}{x^{2}}-9x^{-5}$$

Express \frac{-\frac{1}{27}}{x^{2}} as a single fraction.

$$\frac{-1}{27x^{2}}-9x^{-5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -9x^{-5} times \frac{27x^{2}}{27x^{2}}.

$$\frac{-1}{27x^{2}}+\frac{-9x^{-5}\times 27x^{2}}{27x^{2}}$$

Since \frac{-1}{27x^{2}} and \frac{-9x^{-5}\times 27x^{2}}{27x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-1-9x^{-5}\times 27x^{2}}{27x^{2}}$$

Do the multiplications in -1-9x^{-5}\times 27x^{2}.

$$\frac{-1-243x^{-3}}{27x^{2}}$$

Factor the expressions that are not already factored in \frac{-1-243x^{-3}}{27x^{2}}.

$$\frac{-x^{-3}\left(x^{3}+243\right)}{27x^{2}}$$

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

$$\frac{-\left(x^{3}+243\right)}{27x^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{x^{3}+243}{-27x^{5}}$$