Question
Examine and complete the work simplifying the expression (23)3.
1. Expand using 3 factors of 23: (23)(23)(23)
2. Apply the product of a power: 23 + 3 + 3
3. Simplify: 2x
Answer the questions about simplifying and evaluating the expression (23)3 .
What is the value of x in the simplified power?
What is the value of the expression?
1. Expand using 3 factors of 23: (23)(23)(23)
2. Apply the product of a power: 23 + 3 + 3
3. Simplify: 2x
Answer the questions about simplifying and evaluating the expression (23)3 .
What is the value of x in the simplified power?
What is the value of the expression?
Answers
GPT-4o mini
Let's carefully simplify the expression \( (23)^3 \).
1. **Expand using 3 factors of 23**:
\[
(23)^3 = (23)(23)(23)
\]
2. **Apply the product of a power**:
We need to clarify this step. The product of a power rule usually addresses powers of the same base, and in this case, it seems there was a misunderstanding. For numerical values, we will instead multiply:
\[
23 \times 23 \times 23
\]
3. **Now let's compute \( 23 \times 23 \)**:
\[
23 \times 23 = 529
\]
4. **Now multiply by 23 again**:
\[
529 \times 23 = 12167
\]
Thus, we find that:
- The value of \( (23)^3 \) simplifies to \( 12167 \).
### Answering the Questions:
**What is the value of \( x \) in the simplified power?**
- The expression (23)^3 is \( 23^3 \), but your solution seems to suggest a different approach to finding \( x \). The correct form involves using exponent laws, but there isn’t an explicit \( x \) as the exponents correspond to the numbers directly. Therefore, **there is no value of \( x \)** in a simplified context.
**What is the value of the expression?**
- The value of the expression \( (23)^3 \) is \( 12167 \).
1. **Expand using 3 factors of 23**:
\[
(23)^3 = (23)(23)(23)
\]
2. **Apply the product of a power**:
We need to clarify this step. The product of a power rule usually addresses powers of the same base, and in this case, it seems there was a misunderstanding. For numerical values, we will instead multiply:
\[
23 \times 23 \times 23
\]
3. **Now let's compute \( 23 \times 23 \)**:
\[
23 \times 23 = 529
\]
4. **Now multiply by 23 again**:
\[
529 \times 23 = 12167
\]
Thus, we find that:
- The value of \( (23)^3 \) simplifies to \( 12167 \).
### Answering the Questions:
**What is the value of \( x \) in the simplified power?**
- The expression (23)^3 is \( 23^3 \), but your solution seems to suggest a different approach to finding \( x \). The correct form involves using exponent laws, but there isn’t an explicit \( x \) as the exponents correspond to the numbers directly. Therefore, **there is no value of \( x \)** in a simplified context.
**What is the value of the expression?**
- The value of the expression \( (23)^3 \) is \( 12167 \).