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footprints
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[tex]3y^{\frac{2}{3}}=x[/tex]
How do I make y the subject?
[tex]y^{\frac{2}{3}}=\frac{x}{3}[/tex]
Then what?
How do I make y the subject?
[tex]y^{\frac{2}{3}}=\frac{x}{3}[/tex]
Then what?
How did you go from [tex]\sqrt[\frac{2}{3}]{\frac{x}{3}}[/tex] to [tex]\sqrt{(\frac{x}{3})^{3}}[/tex][tex]y = \sqrt[\frac{2}{3}]{\frac{x}{3}} = \sqrt{(\frac{x}{3})^{3}}[/tex]
footprints said:How did you go from [tex]\sqrt[\frac{2}{3}]{\frac{x}{3}}[/tex] to [tex]\sqrt{(\frac{x}{3})^{3}}[/tex]
Oh ya! Forgot about that.Nylex said:Using the law of indicies that says a^mn = (a^m)^n.
y^(2/3) = x/3
Cube both sides: y^2 = (x/3)^3
Now square root both sides: y = (x/3)^3/2 = [(x/3)^3]^1/2, which is what you have (I can't use LaTeX properly, oops).
Making y the subject involves using algebraic manipulation to isolate y on one side of the equation. This can be done by performing inverse operations on both sides of the equation until y is the only term on one side.
In most cases, yes. As long as the equation follows mathematical rules and has a unique solution, y can be solved for. However, some equations may have no solution or infinite solutions.
The most common steps for making y the subject include: identifying what operations are currently being performed on y, performing the inverse of those operations on both sides of the equation, and simplifying the equation until y is the only term remaining on one side.
If there are multiple y terms in the equation, try to combine them into one term by factoring out the common factor. Then, follow the usual steps for making y the subject. If it is not possible to combine the y terms, you may need to use more advanced algebraic techniques.
Yes, it is important to follow the order of operations (PEMDAS) when solving equations and making y the subject. This means performing operations in the following order: parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).