Question
What is the following expression equivalent to? \( \left(b^{3}\right)^{4} b^{5} \) \( b^{23} \) \( b^{12} \) \( b^{60} \) \( b^{17} \)
Ask by Li Blake. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression \( \left(b^{3}\right)^{4} b^{5} \) simplifies to \( b^{17} \).
Solution
To simplify the expression \( \left(b^{3}\right)^{4} b^{5} \), follow these steps:
1. **Apply the Power of a Power Rule**:
\[
\left(b^{3}\right)^{4} = b^{3 \times 4} = b^{12}
\]
2. **Multiply the Result by \( b^{5} \)**:
\[
b^{12} \times b^{5} = b^{12 + 5} = b^{17}
\]
So, the expression \( \left(b^{3}\right)^{4} b^{5} \) is equivalent to \( b^{17} \).
**Answer:** \( b^{17} \)
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Simplify this solution Bonus Knowledge
To simplify the expression \( \left(b^{3}\right)^{4} b^{5} \), you first use the power of a power rule, which states that \( (x^m)^n = x^{m \cdot n} \). Thus, \( \left(b^{3}\right)^{4} = b^{3 \cdot 4} = b^{12} \). Now, you combine that with \( b^{5} \). Using the product of powers rule \( x^m \cdot x^n = x^{m+n} \), you get \( b^{12} \cdot b^{5} = b^{12 + 5} = b^{17} \). So, the expression is equivalent to \( b^{17} \).
