Solve left(5x^-4-3right)^3

$${ \left(5 { x }^{ -4 } -3 \right) }^{ 3 }$$

Evaluate

$$\frac{\left(5-3x^{4}\right)^{3}}{x^{12}}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5x^{-4}-3\right)^{3}.

$$125\left(x^{-4}\right)^{3}-225\left(x^{-4}\right)^{2}+135x^{-4}-27$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$125x^{-12}-225\left(x^{-4}\right)^{2}+135x^{-4}-27$$

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

$$125x^{-12}-225x^{-8}+135x^{-4}-27$$

Expand

$$-27+\frac{135}{x^{4}}-\frac{225}{x^{8}}+\frac{125}{x^{12}}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5x^{-4}-3\right)^{3}.

$$125\left(x^{-4}\right)^{3}-225\left(x^{-4}\right)^{2}+135x^{-4}-27$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$125x^{-12}-225\left(x^{-4}\right)^{2}+135x^{-4}-27$$

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

$$125x^{-12}-225x^{-8}+135x^{-4}-27$$