Questions: Write y^2 * y^5 without exponents. y^2 * y^5= Fill in the blank. y^2 * y^5=y^

Transcript text: Write $y^{2} \cdot y^{5}$ without exponents. $\square$ $y^{2} \cdot y^{5}=$ $\square$ Fill in the blank. $y^{2} \cdot y^{5}=y^{\square}$

Solution

Solution Steps

Step 1: Apply the Law of Exponents

When multiplying two expressions with the same base, you add their exponents. That is: \[ y^{a} \cdot y^{b} = y^{a + b} \]

Step 2: Add the Exponents

For the given expression $ y^{2} \cdot y^{5} $, add the exponents $ 2 $ and $ 5 $: \[ y^{2} \cdot y^{5} = y^{2 + 5} \]

Step 3: Simplify the Exponent

Simplify the exponent: \[ y^{2 + 5} = y^{7} \]

Final Answer

\[ \boxed{y^{2} \cdot y^{5} = y^{7}} \]

The blank should be filled with $ 7 $: \[ y^{2} \cdot y^{5} = y^{\boxed{7}} \]

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