To solve for x algebraically, we need to isolate x by getting rid of the exponent of $\frac{2}{3}$. To remove the exponent, we can raise both sides of the equation to the power of $\frac{3}{2}$:
\begin{aligned}
\left(x+2\right)^{\frac{2}{3}} &=9 \\
\left(\left(x+2\right)^{\frac{2}{3}}\right)^{\frac{3}{2}} &=9^{\frac{3}{2}} \\
\left(x+2\right)^{\frac{2}{3}\cdot\frac{3}{2}} &=27 \\
\left(x+2\right)^1 &=27 \\
x + 2 &= 27 \\
x &= 27 - 2 \\
x &= 25
\end{aligned}
Therefore, the solution to the equation is x = 25.
Solve algebraically showing all steps.
\left(x+2\right)^{\frac{2}{3}}=9
1 answer