Simplify the Expression: y^9 ÷ y^3 Using Exponent Rules

To solve the expression $\frac{y^9}{y^3}$, we will apply the rules of exponents, specifically the power of division rule, which states that when you divide like bases, you subtract the exponents.

Here are the steps to arrive at the solution:

• Step 1: Identify and write down the expression: $\frac{y^9}{y^3}$.

• Step 2: Apply the division rule of exponents, which is $\frac{a^m}{a^n} = a^{m-n}$, for any non-zero base $a$.

• Step 3: Using the division rule, subtract the exponent in the denominator from the exponent in the numerator:$y^{9-3}$

• Step 4: Calculate the exponent: $9 - 3 = 6$

• Step 5: Write down the simplified expression:$y^6$

Therefore, the expression $\frac{y^9}{y^3}$ simplifies to $y^6$.