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For any two non-zero integers x and y, x3 ÷ y3 is equal to

This question was previously asked in
Bihar STET Paper I: Mathematics (Held In 2019 - Shift 1)
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  1. \(\rm\left(\frac{x}{y}\right)^0\)
  2. \(\rm\left(\frac{x}{y}\right)^3 \)
  3. \(\rm\left(\frac{x}{y}\right)^6\)
  4. \(\rm\left(\frac{x}{y}\right)^9\)

Answer (Detailed Solution Below)

Option 2 : \(\rm\left(\frac{x}{y}\right)^3 \)
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Detailed Solution

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Explanation:

For any two non-zero integers x and y, x³ ÷ y³ is equal to: (x/y)³
This is because of the properties of exponents.

When dividing two numbers with the same exponent, you can write it as the ratio of the bases raised to the power of the exponent.

Hence, (x³ ÷ y³) = (x/y)³.

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