Question

Simplify (x^12/x^3)^1/3

Answer 1

x^3

Explanation:

To simplify the expression
`\(\left((x^(12))/(x^3)\right)^{(1)/(3)}\)`, you can use the properties of exponents.

1. Apply the division rule for exponents:
`\(a^m / a^n = a^(m-n)\)`.

`\[ (x^(12))/(x^3) = x^(12-3) = x^9 \]`

2. Now, you have
`\((x^9)^{(1)/(3)}\)`.

3. Apply the power rule for exponents:
`\((a^m)^n = a^(m \cdot n)\)`.

`\[ (x^9)^{(1)/(3)} = x^{9 \cdot (1)/(3)} \]`

4. Simplify the exponent by multiplying:

`\[ x^{9 \cdot (1)/(3)} = x^3 \]`

So,
`\(\left((x^(12))/(x^3)\right)^{(1)/(3)}\)` simplifies to
`\(x^3\)`.