I was presented with the question: $$(\frac{x}{a})^{3.2} + (\frac{y}{b})^{3.2} = 1$$  While: $$\frac{a}{b} = \frac{174.1}{86}=c$$  I began to simplify and reached: $$x = c(b^{3.2}-y^{3.2})^{1/3.2}$$ $$y = \frac{(a^{3.2} - x^{3.2})^{1/3.2}}{c}$$ My goal is to solve for $x$. Thus, I substituted $y$: $$x = c(b^{3.2}-(b^{3.2}-((\frac{x^{3.2}}{c^{3.2}})^{1/3.2})^{3.2})^{1/3.2}$$ I then simplify: $$x = c(b^{3.2}-(b^{3.2}-(\frac{x^{3.2}}{c^{3.2}}))^{1/3.2}$$  How should I proceed? I am looking for $x =$
I'm hoping someone could check my work. I'm trying to simplify the equation for $x$. $$(\frac{x}{a})^{3.2} + (\frac{y}{b})^{3.2} = 1$$ $$\frac{a}{b} = \frac{174.1}{86}$$ Thus I began by substituting $a$ with: $$a = \frac{174.1}{86}b$$ $$((\frac{86}{174.1})(\frac{x}{b}))^{3.2} + (\frac{y}{b})^{3.2} = 1$$ $$((\frac{86}{174.1})(\frac{x}{b}))^{3.2} = 1 - (\frac{y}{b})^{3.2}$$ $$(\frac{x}{b})^{3.2} = \frac{(1 - (\frac{y}{b})^{3.2})(174.1)^{3.2}}{(86)^{3.2}}$$ $$x^{3.2} = \frac{(1 - (\frac{y}{b})^{3.2})(174.1)^{3.2}(b)^{3.2}}{(86)^{3.2}}$$ $$x^{3.2} = \frac{(1 - (\frac{y}{b})^{3.2})((174.1)(b))^{3.2}}{(86)^{3.2}}$$ $$x^{\frac{16}{5}} = \frac{(1 - (\frac{y}{b})^{3.2})((174.1)(b))^{3.2}}{(86)^{3.2}}$$ $$x = [\frac{(1 - (\frac{y}{b})^{3.2})((174.1)(b))^{3.2}}{(86)^{3.2}}]^{\frac{5}{16}}$$ Is my work correct, or am I completely off the board?
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