Question

X to the second power equals 32 divided by 121

Answer 1

To solve the equation x² = 32/121, take the square root of both sides leading to x = ±4/11 as the solution. This is achieved by simplifying the square root of the fraction.

Step-by-step explanation:

You asked about solving the equation x to the second power equals 32 divided by 121. To find the value of x, you would take the square root of both sides of the equation. Here's the step-by-step process:

1. Write down the equation: x² = 32/121.
2. Take the square root of both sides to get x = ±√(32/121).
3. Since 32 is 2 to the power of 5, and 121 is 11 squared, we can simplify the roots as x = ±√(2⁵/11²).
4. Now, taking the square root of both numbers under the root leads to x = ±(2⁵/²)/(11²/²), which simplifies to x = ±(2²/11).
5. Thus, x = ±4/11 is the solution to your equation.

This kind of problem is fundamental in algebra, where we often manipulate exponents and roots. Remember that the square root of a fraction is the square root of the numerator divided by the square root of the denominator, and for negative exponents, like in 2.4 x 10^-2, you move the decimal place to the left by the number of negative exponent digits to get the correct 0.024 answer.