To solve the expression [tex]\[(46 \cdot 59)^6\][/tex] using the same bases, we can utilize the properties of exponents. Specifically, we leverage the property that states:
[tex]\[(a \cdot b)^n = a^n \cdot b^n\][/tex]
Here, our bases are 46 and 59, and the exponent is 6. Let's break it down into steps:
1. Identify the bases and the exponent:
- Base 1: 46
- Base 2: 59
- Exponent: 6
2. Apply the property of exponents:
- Rewrite the expression [tex]\((46 \cdot 59)^6\)[/tex] using the property:
[tex]\[(46 \cdot 59)^6 = 46^6 \cdot 59^6\][/tex]
Therefore, the equivalent expression is [tex]\(46^6 \cdot 59^6\)[/tex].
3. Calculate the values (already given):
- [tex]\(46^6 = 9474296896\)[/tex]
- [tex]\(59^6 = 42180533641\)[/tex]
So, the final expression with the values plugged in is:
[tex]\[(46^6, 59^6) = (9474296896, 42180533641)\][/tex]
Thus, the correct answer is:
[tex]\[
946820121456896, (9474296896, 42180533641)
\][/tex]
