Answer: x*x*x is equal to x3 (read as “x cubed” or “x to the power 3”). When x is multiplied by itself three times, we write it in short form as x3. It is not equal to 3x.
Why is x*x*x Equal to x3?
In maths, the power (exponent) tells how many times a number is multiplied by itself. Since x appears three times in x*x*x, the power is 3.
| Expression | Short Form | Read As |
|---|---|---|
| x | x1 | x |
| x*x | x2 | x squared |
| x*x*x | x3 | x cubed |
| x*x*x*x | x4 | x to the power 4 |
| x*x*x*x*x | x5 | x to the power 5 |
x*x*x vs x+x+x: What is the Difference?
Multiplication and addition give different results:
- x*x*x = x3 (x multiplied three times)
- x+x+x = 3x (x added three times)
Example: if x = 2, then x*x*x = 2 × 2 × 2 = 8, but x+x+x = 2 + 2 + 2 = 6. So x3 and 3x are only equal when x = 0 or x = ±√3.
Values of x*x*x for Different Numbers
| Value of x | x*x*x | Result (x3) |
|---|---|---|
| 1 | 1 × 1 × 1 | 1 |
| 2 | 2 × 2 × 2 | 8 |
| 3 | 3 × 3 × 3 | 27 |
| 4 | 4 × 4 × 4 | 64 |
| 5 | 5 × 5 × 5 | 125 |
| 10 | 10 × 10 × 10 | 1000 |
| −2 | (−2) × (−2) × (−2) | −8 |
Solved Examples: Find x When x*x*x is Given
If x*x*x equals a number, then x is the cube root of that number (x = ∛n).
x*x*x is Equal to 2024
x3 = 2024
x = ∛2024 ≈ 12.6494
2024 is not a perfect cube, because 123 = 1728 and 133 = 2197. So x lies between 12 and 13. Check: 12.64943 ≈ 2024.00 ✔
x*x*x is Equal to 2025
x3 = 2025
x = ∛2025 ≈ 12.6515
x*x*x is Equal to 2026
x3 = 2026
x = ∛2026 ≈ 12.6536
x*x*x is Equal to 8, 27 or −8
- x3 = 8 → x = 2
- x3 = 27 → x = 3
- x3 = −8 → x = −2 (a negative number cubed stays negative)
x*x*x is Equal to x
x3 = x
x3 − x = 0
x(x2 − 1) = 0
x(x − 1)(x + 1) = 0
So x = 0, 1 or −1.
x*xxx*x is Equal to x
Here x*xxx*x means x × x × x × x × x = x5. So the equation is x5 = x.
x5 − x = 0
x(x4 − 1) = 0
x(x2 − 1)(x2 + 1) = 0
Since x2 + 1 can never be 0 for a real number, the real solutions are x = 0, 1 or −1.
Common Mistakes Students Make
- Writing x*x*x = 3x. Correct: x*x*x = x3; only x+x+x = 3x.
- Writing x*x*x = x2. Count the x’s: three x’s means power 3.
- Thinking (−x)3 is positive. A negative number raised to an odd power stays negative.
FAQs on x*x*x is Equal To
What is x*x*x equal to?
x*x*x is equal to x3, which means x multiplied by itself three times.
Is x*x*x equal to 3x?
No. x*x*x = x3 while x+x+x = 3x. For example, when x = 3, x3 = 27 but 3x = 9.
What is x*x*x*x equal to?
x*x*x*x is equal to x4 (x to the power 4).
If x*x*x = 2024, what is x?
x is the cube root of 2024, which is about 12.6494.
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