To find the solution to the equation x³ = 9 × 27, let’s first simplify the right side of the equation.
Calculating 9 × 27 gives us:
9 × 27 = 243
Now we have the equation x³ = 243.
To solve for x, we take the cube root of both sides:
x = ∛243
Next, we need to determine the cube root of 243. We can break it down into prime factors:
243 = 3 × 3 × 3 × 3 × 3 = 3^5
The cube root can be expressed as:
∛(3^5) = 3^(5/3) = 3^(1 + 2/3)
This means we have:
3 × ∛(3^2)
Since 3^2 = 9, we have:
3 × ∛9
However, for our purposes, we can also simply calculate the cube root of 243 directly, which gives us:
x = 9
In conclusion, the solution to x³ = 9 × 27 is x = 9.