# Solve 54x^3-16=0.

#### sprink268

How do I solve for this problem

54x^3-16=0

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#### Prove It

MHF Helper
How do I solve for this problem

54x^3-16=0
Assuming $$\displaystyle x$$ is real...

$$\displaystyle 54x^3 = 16$$

$$\displaystyle x^3 = \frac{16}{54}$$

$$\displaystyle x^3 = \frac{8}{27}$$

$$\displaystyle x = \sqrt[3]{\frac{8}{27}}$$

$$\displaystyle x = \frac{\sqrt[3]{8}}{\sqrt[3]{27}}$$

$$\displaystyle x = \frac{2}{3}$$.

sprink268

#### Chris L T521

MHF Hall of Fame
How do I solve for this problem

54x^3-16=0
Solve for $$\displaystyle x^3$$ and then take the cube root of both sides.

$$\displaystyle 54x^3-16=0\implies x^3=\frac{16}{54}=\frac{8}{27}$$

Thus, $$\displaystyle x=\sqrt[3]{\frac{8}{27}}=\ldots$$.

Can you simplify this result?

sprink268