solve for x: x^-4/3=81

Question

a) -27

b) -1/27

c) 1/27

d) 27

Answer 1

x^-4/3=81

1/(x^.333)^4=81

1/(x^.333)=3

1=3(x^.333)

x^.333=.333

x=.03703692......

Answer 2

To determine this answer, we first need to recognize what fractional exponents are, and how we go about interpreting them.

We know that x² is simply taking the variable x, and squaring it. Another way we could write that is x^2/1 . In other words, the numerator (top number) of a fractional exponent is the "power" that you are raising it to, and the denominator (bottom number) of a fractional exponent is "root" which you are taking.

As with other algebraic manipulations, in order to undo an operation to solve for a variable, you must do the opposite. In our example, we have x^-4/3=81. To solve for x, we must first cube both sides of the equation, or in other words, raise each side to the third power. This will eliminate the 3 in the fractional exponent on the left-hand side.

We re-write as:

x^-4=81³

^{Further re-writing this (negative exponents can be flipped to the denominator if they're on top, or flipped to the numerator if they're on the bottom.}

1/(x⁴)=81³

Further algebraic manipulation (cross multiplying to get the x on top), we re-write as:

1/81³=x⁴

To undo a power, in this case, x⁴ we need to take the fourth root. Thus, we find that:

x=(1/81³)^1/4

Therefore, x=1/27