Question

Identify all equivalent expressions:

(12a3)0(14b)2


Responses

(12)0×a3x0×(14)2×b2
(12)0×a3x0×(14)2×b2

1×1×14×14×b×b
1×1×14×14×b×b

0
0

(12)0×a3+0×(14)2×b2
(12)0×a3+0×(14)2×b2

116b2
1 over 16 b squared

0×0×14×14×b×b

Answer 1

To identify equivalent expressions for \((12a^3)^{0}(14b)^{2}\), let's simplify it step by step.

1. **Calculate each part**:
- \((12a^3)^{0} = 1\) (Any non-zero quantity raised to the power of 0 is 1).
- \((14b)^{2} = 196b^{2}\) (You square both 14 and b).

Putting the simplified parts together:

\[
(12a^{3})^{0}(14b)^{2} = 1 \times 196b^{2} = 196b^{2}
\]

Now, let's analyze the provided options for any equivalent expressions:

1. **First option** \( (12)^{0} \times a^{3} \times (14)^{2} \times b^{2}\):
- \((12)^{0} = 1\), thus this simplifies to \(1 \times a^{3} \times 196 \times b^{2} = 196a^{3}b^{2}\), which is not equivalent.

2. **Second option** \( 1 \times 1 \times 14 \times 14 \times b \times b \):
- This simplifies to \(1 \times 1 \times 196 \times b^{2} = 196b^{2}\), which is equivalent.

3. **Third option** \( 0 \):
- This is not equivalent.

4. **Fourth option** \( (12)^{0} \times a^{3} + 0 \times (14)^{2} \times b^{2} \):
- The first term simplifies to \(1 \times a^{3} = a^{3}\), and the second term is \(0\), thus \(a^{3} + 0 = a^{3}\), which is not equivalent.

5. **Fifth option** \( 1/16 b^{2} \):
- This is simplified to \(0\) which is not equivalent.

6. **Sixth option** \( 0 \times 0 \times 14 \times 14 \times b \times b \):
- This is also \(0\), which is not equivalent.

### Summary of Equivalent Expressions:
- The equivalent expression for \((12a^{3})^{0}(14b)^{2}\) is:
- \(1 \times 1 \times 14 \times 14 \times b \times b\) (which simplifies to \(196b^{2}\)).

Thus, the only equivalent expression is:
- \(1\times 1\times 14\times 14\times b^{2}\) which simplifies to \(196b^{2}\).