Sure, let's solve the equation step by step.

Given equation:
$$
(x - 6)^{2/3} + 1 = 10
$$

Step 1: Subtract 1 from both sides to isolate the term with the exponent.
$$
(x - 6)^{2/3} = 9
$$

Step 2: Raise both sides to the power of $\frac{3}{2}$ to eliminate the fractional exponent.
$$
\left((x - 6)^{2/3}\right)^{3/2} = 9^{3/2}
$$

Step 3: Simplify both sides.
$$
x - 6 = 9^{3/2}
$$

Step 4: Calculate $9^{3/2}$.
$$
9^{3/2} = (9^1)^{3/2} = 9^{1.5} = (3^2)^{1.5} = 3^3 = 27
$$

Step 5: Add 6 to both sides to solve for $x$.
$$
x - 6 = 27
$$
$$
x = 27 + 6
$$
$$
x = 33
$$

So, the solution to the equation is:
$$
x = 33
$$

Question

Sure, let's solve the equation step by step.

Given equation:
$$
(x - 6)^{2/3} + 1 = 10
$$

Step 1: Subtract 1 from both sides to isolate the term with the exponent.
$$
(x - 6)^{2/3} = 9
$$

Step 2: Raise both sides to the power of $\frac{3}{2}$ to eliminate the fractional exponent.
$$
\left((x - 6)^{2/3}\right)^{3/2} = 9^{3/2}
$$

Step 3: Simplify both sides.
$$
x - 6 = 9^{3/2}
$$

Step 4: Calculate $9^{3/2}$.
$$
9^{3/2} = (9^1)^{3/2} = 9^{1.5} = (3^2)^{1.5} = 3^3 = 27
$$

Step 5: Add 6 to both sides to solve for $x$.
$$
x - 6 = 27
$$
$$
x = 27 + 6
$$
$$
x = 33
$$

So, the solution to the equation is:
$$
x = 33
$$

Knowee AI · Accepted Answer