Question

which answer is correct?

6^2 . 6^5 = 36^8 6^2 . 6^5 = 6^10 6^2 . 6^5 = 6^7

Answer 1

what did the other two do wrong in their answers?

Answer 2

To solve the equation \(6^2 \cdot 6^5\), we can use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).

Thus, we have:

\[
6^2 \cdot 6^5 = 6^{2 + 5} = 6^7
\]

Now let's evaluate your options:

1. \(6^2 \cdot 6^5 = 36^8\): This is incorrect.
2. \(6^2 \cdot 6^5 = 6^{10}\): This is incorrect.
3. \(6^2 \cdot 6^5 = 6^7\): This is correct.

So, the correct answer is \(6^2 \cdot 6^5 = 6^7\).

Answer 3

Let's examine what went wrong in the incorrect answers:

1. **\(6^2 \cdot 6^5 = 36^8\)**:
- This answer mistakenly equates \(6^2 \cdot 6^5\) to \(36^8\).
- To break this down, \(36\) can be expressed as \(6^2\), so \(36^8\) is equivalent to \((6^2)^8 = 6^{16}\). Therefore, \(36^8\) equals \(6^{16}\), not \(6^7\). This option does not apply the properties of exponents correctly.

2. **\(6^2 \cdot 6^5 = 6^{10}\)**:
- This answer incorrectly adds the exponents. The correct application of the exponent property states that we should add the exponents, which in this case is \(2 + 5 = 7\), not \(10\). Thus, \(6^{10}\) (which would imply \(2 + 5 = 10\)) is incorrect.
- Rather, \(6^2 \cdot 6^5\) correctly simplifies to \(6^7\).

In summary, the first incorrect answer fails by misinterpreting the bases and exponents, while the second incorrect answer simply adds the exponents incorrectly. The correct application leads us to \(6^7\).