To determine what (4/5)⁶ equals, let's use the exponentiation rule for division:
When you have a fraction raised to a power, you can apply that power to both the numerator and the denominator separately.
In mathematical terms:
(a/b)ⁿ = aⁿ / bⁿ
Where:
- a is the numerator
- b is the denominator, and b ≠ 0
- n is the exponent
Applying this to the given fraction (4/5):
(4/5)⁶ = 4⁶ / 5⁶
Therefore, the correct answer to "(4/5)⁶ is equal to" is A) 4⁶/5⁶.
Let's also check why the other options are incorrect:
B) 24/30 is not equivalent to (4/5)⁶, because although 24/30 reduces to 4/5 when simplified, raising it to the 6th power is not the same as simply presenting the fraction.
C) 4⁶/5 is incorrect because only the numerator 4 is raised to the 6th power, not the denominator.
D) 6 x (4/5) is incorrect because this suggests multiplying 4/5 by 6, which is not the same as raising 4/5 to the 6th power.
So, the correct and complete answer is:
(4/5)⁶ is equal to 4⁶/5⁶.