Solve each equation. Round answers to the nearest hundredth as needed. x^(2/3) =36

Question

Accepted Answer

Hello, everyone. In the given equation we've been asked to solve for X. The equation is X raised to the eight thirds power equals 256. Our answer choices are a negative four and four B negative eight and eight C negative 16 and 16 D negative 64. First, I'm gonna rewrite the equation. So if X raised the eight thirds power equals 256 and I wanna see if I can get 256 to have an exponent of eight, that way I could simplify my exponents a little quicker. So X rays to the eight thirds power and then when I try to simplify 256 I find that that is too raised to the eighth power. This helps us because now we can take the eighth route of both sides, which is the same as raising both of our bases to the 1/8 power. And when we do that, we can cross reduce our, our exponent fractions. So we get X raised to the one third power equals two, raise the first power, which is the same as two, one thing. However, is we want this to be a plus or minus two because we don't know which one was raised to the eighth power to get our 256. So I'm going to put a plus or minus in front of this two. So it's either a positive two or a negative two next to eliminate the one third as an exponent on the X, I'm going to cube both sides. So I'm raising them both to the third power. Again, my exponents will reduce, leaving me with X and then positive two raised to the third power is eight, negative two reads to the third power is negative eight. So we have two X values, it could be negative eight or positive eight and that matches answer choice B have a nice day.

Solve each equation. Round answers to the nearest hundredth as needed. x^(2/3) =36

Verified Solution

Key Concepts

Exponents and Fractional Powers

Isolating the Variable

Rounding and Significant Figures