Answer:
A: x = 0
B: x = All real numbers
Explanation:
A.
Any number to the power of (0) equals one. This applies true for the given situation; one is given an expression which is as follows;
![(6^2)^x=1](https://img.qammunity.org/2022/formulas/mathematics/college/r3xo3e9tiv06t31zjmh5w8nvgupp2zkeow.png)
Simplifying that will result in;
![36^x=1](https://img.qammunity.org/2022/formulas/mathematics/college/jty1hs1qqnnyqrnud58i1iysvv0mrieqa8.png)
As stated above, any number to the power of (0) equals (1), thus (x) must equal (0) for this equation to hold true.
![36^0=1\\x=0](https://img.qammunity.org/2022/formulas/mathematics/college/v433kk6zaj9t9381mknthmajy7kpv33h7t.png)
B.
As stated in part (A), any number to the power (0) equals (1). Therefore, when given the following expression;
![(6^0)^x=1](https://img.qammunity.org/2022/formulas/mathematics/college/6hp39a3bc0bi9wgjzkhfna7ytus0zwiwuc.png)
One can simplify that;
![1^x=1](https://img.qammunity.org/2022/formulas/mathematics/college/9802bvc8q6vqf9a4nmcs3cpqng0f0p5cbb.png)
However, (1) to any degree still equals (1). Thus, (x) can be any value, and the equation will still hold true.
![x=All\ real \ numbers](https://img.qammunity.org/2022/formulas/mathematics/college/5qettn4tn3w1q2zyd3pqt7mo0s64sp01i0.png)