Solve (5x^-1-3)^3

$$( 5 x ^ { - 1 } - 3 ) ^ { 3 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5x^{-1}-3\right)^{3}.

$$125\left(x^{-1}\right)^{3}-225\left(x^{-1}\right)^{2}+135x^{-1}-27$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$125x^{-3}-225\left(x^{-1}\right)^{2}+135x^{-1}-27$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$125x^{-3}-225x^{-2}+135x^{-1}-27$$

Expand

$$-27+\frac{135}{x}-\frac{225}{x^{2}}+\frac{125}{x^{3}}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5x^{-1}-3\right)^{3}.

$$125\left(x^{-1}\right)^{3}-225\left(x^{-1}\right)^{2}+135x^{-1}-27$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$125x^{-3}-225\left(x^{-1}\right)^{2}+135x^{-1}-27$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$125x^{-3}-225x^{-2}+135x^{-1}-27$$