Question
Question 12 A) \( x^{8} \cdot x^{5}=x^{p} \) where \( p=\square\langle \rangle \) B) \( \left(x^{8}\right)^{5}=x^{r} \) where \( r=\square \)
Ask by Reyes Santiago. in the United States
Mar 07,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A) \( p = 13 \)
B) \( r = 40 \)
Solution
Solve the equation by following steps:
- step0: Solve for \(p\):
\(8+5=p\)
- step1: Add the numbers:
\(13=p\)
- step2: Swap the sides:
\(p=13\)
Solve the equation \( 8*5=r \).
Solve the equation by following steps:
- step0: Solve for \(r\):
\(8\times 5=r\)
- step1: Multiply the numbers:
\(40=r\)
- step2: Swap the sides:
\(r=40\)
Let's solve each part step by step.
### A) \( x^{8} \cdot x^{5}=x^{p} \)
Using the property of exponents that states \( x^{a} \cdot x^{b} = x^{a+b} \), we can combine the exponents:
\[
p = 8 + 5
\]
Calculating this gives:
\[
p = 13
\]
So, the answer for part A is \( p = 13 \).
### B) \( \left(x^{8}\right)^{5}=x^{r} \)
Using the property of exponents that states \( (x^{a})^{b} = x^{a \cdot b} \), we can simplify this expression:
\[
r = 8 \cdot 5
\]
Calculating this gives:
\[
r = 40
\]
So, the answer for part B is \( r = 40 \).
### Summary of Answers:
- A) \( p = 13 \)
- B) \( r = 40 \)
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Simplify this solution Extra Insights
When multiplying powers with the same base, you add the exponents. Therefore, for \(x^{8} \cdot x^{5}\), you get \(x^{8+5}=x^{13}\). So, \(p=13\)! For exponentiation, you multiply the exponents. In this case, \(\left(x^{8}\right)^{5}\) equals \(x^{8 \cdot 5}=x^{40}\). Thus, \(r=40\)!
