Which expressions are equivalent to 2 to the power of 5 / 6 to the power of 5

1. 1/3

2. 3 to the power of - 5

3. (-4) to the power of - 5

4. 2 to the 5th power times 6 to the - 5 power

2. 3 to the power of - 5

4. 2 to the 5th power times 6 to the - 5 power

Step-by-step explanation:

(2⁵) / (6⁵)

(2/6) ⁵

(1/3) ⁵

(3^-1) ⁵

3^ (-5)

(2/6) ⁵

2⁵ * (6^-1) ⁵

2⁵ * (6^-5)

Steps to solve:

2^5/6^5

~Apply exponent rules

(1/3) ^5

1^5/3^5

~Simplify

1/243

Now, we can solve for each option.

Option 1:

1/3 ≠ 1/243

This is incorrect.

Option 2:

3^-5 = 1/243

This is correct.

Option 3:

-4^-5

-1/4^5

-1/1024 ≠ 1/243

This is incorrect.

Option 4:

2^5 * 6^-5

2^5 * 1/6^5

2^5/6^5

1^5/3^5

1/243 = 1/243

This is correct.

Therefore, the correct answers are options 2 and 4.

Best of Luck!