Question
Write \( p^{3} \cdot p \) without exponents. \( p^{3} \cdot p=\prod \) Fill in the blank. \( p^{3} \cdot p=p \)
Ask by Weaver Frank. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( p^{3} \cdot p = p \cdot p \cdot p \cdot p \)
Solution
To write \( p^{3} \cdot p \) without exponents, we can use the property of exponents that states when multiplying like bases, we add the exponents.
Here, we have:
\[
p^{3} \cdot p = p^{3} \cdot p^{1} = p^{3+1} = p^{4}
\]
Thus, the expression \( p^{3} \cdot p \) can be rewritten as:
\[
p^{3} \cdot p = p \cdot p \cdot p \cdot p
\]
So, filling in the blank, we have:
\[
p^{3} \cdot p = \prod_{i=1}^{4} p
\]
Therefore, the final answer is:
\[
p^{3} \cdot p = p \cdot p \cdot p \cdot p
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
The product can be expressed as \( p^3 \cdot p = p^{3+1} = p^4 \). In expanded form, this is \( p \cdot p \cdot p \cdot p \). So, \( p^{3} \cdot p = p \cdot p \cdot p \cdot p \).