Questions: Write p^2 * p^5 without exponents. p^2 * p^3= Fill in the blank. p^2 * p^5=p^7

Transcript text: Write $p^{2} \cdot p^{5}$ without exponents. \[ p^{2} \cdot p^{3}= \] $\square$ Fill in the blank. \[ p^{2} \cdot p^{5}=p^{\square} \]

Solution

Solution Steps

To solve the problem of writing $ p^2 \cdot p^5 $ without exponents, we need to understand that $ p^2 $ means $ p \times p $ and $ p^5 $ means $ p \times p \times p \times p \times p $. Therefore, $ p^2 \cdot p^5 $ is the product of seven $ p $'s.

For the second part, we use the product rule of exponents, which states that when multiplying like bases, you add the exponents. Therefore, $ p^2 \cdot p^5 = p^{2+5} = p^7 $.

Step 1: Express $ p^2 \cdot p^5 $ Without Exponents

To express $ p^2 \cdot p^5 $ without using exponents, we expand each term. The expression $ p^2 $ is equivalent to $ p \times p $, and $ p^5 $ is equivalent to $ p \times p \times p \times p \times p $. Therefore, the product $ p^2 \cdot p^5 $ can be written as: \[ p \times p \times p \times p \times p \times p \times p \]

Step 2: Apply the Product Rule of Exponents

The product rule of exponents states that when multiplying like bases, you add the exponents. Thus, for $ p^2 \cdot p^5 $, we add the exponents: \[ p^{2+5} = p^7 \]

Final Answer

$\boxed{7}$

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