Of course! Let's solve each part step-by-step.
### 4) [tex]\(\left(a^3\right)^2\)[/tex]:
To solve this expression, we will use the power rule of exponents, which states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex].
1. Identify the exponents in the expression: [tex]\( m = 3 \)[/tex] and [tex]\( n = 2 \)[/tex].
2. Apply the power rule:
[tex]\[
(a^3)^2 = a^{3 \cdot 2}
\][/tex]
3. Multiply the exponents:
[tex]\[
3 \cdot 2 = 6
\][/tex]
Thus, [tex]\(\left(a^3\right)^2 = a^6\)[/tex].
### 5) [tex]\(b^3 \cdot b^2\)[/tex]:
To solve this expression, we will use the product rule of exponents, which states that [tex]\(b^m \cdot b^n = b^{m + n}\)[/tex].
1. Identify the exponents in the expression: [tex]\( m = 3 \)[/tex] and [tex]\( n = 2 \)[/tex].
2. Apply the product rule:
[tex]\[
b^3 \cdot b^2 = b^{3 + 2}
\][/tex]
3. Add the exponents:
[tex]\[
3 + 2 = 5
\][/tex]
Thus, [tex]\(b^3 \cdot b^2 = b^5\)[/tex].
### Final Result:
- [tex]\(\left(a^3\right)^2 = a^6\)[/tex]
- [tex]\(b^3 \cdot b^2 = b^5\)[/tex]
