power of a fraction property
(a/b)^x = (a^x)/(b^x)
The power of a fraction property states that to raise a fraction to a power, one can raise the numerator and denominator separately to that power.
For example, if we have the fraction 3/5 and we want to raise it to the power of 2, we would do the following:
(3/5)^2 = (3^2)/(5^2) = 9/25
In this case, we squared both the numerator (3) and the denominator (5) separately to arrive at the final result, which is the fraction 9/25.
This property can be applied to any power, whether it is a positive or negative power or even a fractional power. However, it is important to note that if the base fraction is negative, we must always put the fraction in parentheses before raising it to a power to avoid any confusion.
For example, if we have the fraction -2/3 and we want to raise it to the power of 3, we would do the following:
(-2/3)^3 = (-2)^3/(3)^3 = -8/27
Again, we raised the numerator (-2) and the denominator (3) separately to the power of 3, but we put the fraction (-2/3) in parentheses to ensure that we raised the entire fraction to the power of 3 and not just the numerator.
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