This minilesson explains how to solve equations equation involving fractional exponents. To simplify the equation with fractional
exponents, you can use the rules of exponents.
For example,solve the equation x^{1/3}  2 = 25. In general, steps to solve equations with fractional exponents are:
• first isolate the variable and exponents by adding 2 on both sides of the equation and that yields x^{(1/3)} = 27.
• rewrite the exponent. Through exponent rules, we know that a fractional exponent is the same thing as taking a root. So,the x^{(1/3)} in our equation becomes the cubed root of x.
• now get the x term out from under the radical. To do so, raise both sides of the equation to the third power. We now have 27^{3} = x.
• calculate the value of 27^{3}.You get x = = 19683.(More text below video...)
(Continued from above)
In cases, when the equation has two terms of fractional
exponent (one squared of the other), i.e. the equation is in the quadratic form,
first factor the quadratic equation and solve for the resulting variable.
For example, x^{2/3}  5x^{1/3} + 6 = 0, simplifies
to x = 27, 8.
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