Express each power as an equivalent radical.
K. I don't know how to write this, but I'll explain.
There is a fraction. 1 over 9. And 9 has a power up to it which is 5 and a power down which is 3. I don't get how to express this power as an equivalent radical. I checked the answer at the back of the book, and it is 1 over 9 in brackets. beside it there is 1/3 in small font like a power, then there is 5 outside the other brackets. The 5 is a small power.
i'm not sure if i get the picture but do you mean,
1/[9^(5/3)]
if it is, let's focus on the 9^(5/3). let's make 5/3 into 5* 1/3,,
the 5 here means you raise 9 into power of 5, or 9^5,, the 1/3 means "cuberoot" of 9 (thus if it's 1/2, it's "squareroot", and if 1/4, it's "fourth root")
*you must not worry about one since, one raised to any number is still one,,
so there,, hope this helps~ :)
To express a power as an equivalent radical, we need to use the concept of fractional exponents. In this case, the given fraction is 1/9, and the power is 5/3.
To convert this into an equivalent radical, we use the rule:
a^(m/n) = nth root of a^m
Applying this rule, we can express the given power as an equivalent radical:
(1/9)^(5/3) = 3√(1/9)^5
Now, simplifying further, we have:
= 3√(1/9^5)
= 3√(1/9^5)
Since 9 is a perfect square, we can simplify further:
= 3√(1/3^10)
= 3√(1/3^10)
Thus, the equivalent radical form of (1/9)^5/3 is 3√(1/3^10).