Question 12 A) \( x^{8} \cdot x^{5}=x^{p} \) where \( p=\square\langle \rangle \) B) \( \left(x^{8}\right)^{5}=x^{r} \) where \( r=\square \)

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) \( r = 40 \)