Question

Find the quotient.
y⁹ ÷ y³
y^1/3
y³
y⁶
y¹²

Answer 1

`\(y^6\)` because The quotient of (
`\(y^9` ÷
`y^3\`) is
`\(y^6\)`because when dividing powers with the same base, you subtract the exponents.

Step-by-step explanation:

In the given expression (
`\(y^9` ÷
`y^3\`) is
`\(y^6\)`, when dividing two powers with the same base, you subtract the exponents. So,
`\(y^9` ÷
`y^3` =
`y^(9-3) = y^6\)`. This is because when you have the same base (in this case, (y)), and you divide, you subtract the exponent of the divisor from the exponent of the dividend.

The explanation can be further understood by considering the laws of exponents. When you divide powers with the same base, you subtract the exponents because it represents the concept of "canceling out" common factors.

In this case, you're essentially canceling out three \(y\) terms from the numerator with three \(y\) terms from the denominator, leaving you with
`\(y^6\)`.

Therefore, the quotient of (
`\(y^9` ÷
`y^3\`) is
`\(y^6\)`. This means
`\(y^6\)`that is the result when you perform the division operation, and it represents the combined effect of dividing
`\(y^9\)` by
`\(y^3\)`.