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

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, \( p^2 \cdot p^5 = p^{2+5} = p^7 \).

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: \[ p \times p \times p \times p \times p \times p \times p \]

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