Simplify (37)6\left(3^{7}\right)^{6}(37)6. Write your answer in exponential form. (Example: 525^252not 252525 )

Answer 1

To simplify the expression \((37)^6(3^7)^6(37)^6\), we can first use the property of exponents that states \((a^m)(a^n) = a^{m+n}\).

1. Start by analyzing the expression:

   \[ (37)^6(3^7)^6(37)^6 \]

2. We notice that \((37)^6\) appears twice. Thus, we can combine these:

   \[ (37)^6(37)^6 = (37)^{6+6} = (37)^{12} \]

3. Next, simplify \((3^7)^6\) using the property of exponents \((a^m)^n = a^{m \cdot n}\):

   \[ (3^7)^6 = 3^{7 \cdot 6} = 3^{42} \]

4. Now, we can combine everything, so we have:

   \[ (37)^{12}(3^{42}) \]

5. Finally, we can write the expression in exponential form. Since we have two different bases, we cannot simplify it further into a single term. Therefore, our final answer is:

   \[ 37^{12} \cdot 3^{42} \]

So, the simplified expression in exponential form is:

\[ 37^{12} \cdot 3^{42} \]