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

1 Answer

6 votes

Answer:

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
\(x^3\).

User Nikhil Soni
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