Hey , can anyone help me out please? i'm really confused with this problem.
Prove that:
a^(m/n)= n(radical sign) a^m
Any help is appreciated, thank you.
The nth root of a^m is BY DEFINITION a^(m/n)
If you want a more convincing "proof", raise both sides of the equation to the nth power.
The left side is a^(m/n) multiplied by itgself n times, yielding a^m.
The right side is also a^m, because you started out with the nth root of that quantity.
ok, thanx mate
Sure! I can help you with that. To prove the given equation, we can start by expressing both sides of the equation in terms of exponents.
Let's begin with the left-hand side (LHS) of the equation: a^(m/n).
To understand this, let's recall the property of exponents, which states that (a^m)^n = a^(m * n). Applying this property, we can rewrite a^(m/n) as (a^(m/n))^n.
Now, let's simplify (a^(m/n))^n. By using the property (a^m)^n = a^(m * n), we can rewrite it as a^(m * n/n), which reduces to a^m.
So, we have simplified the left-hand side (LHS) of the equation to a^m.
Now, let's move on to the right-hand side (RHS) of the equation: n√(a^m).
The n√ symbol represents the nth root. Thus, n√(a^m) is equivalent to (a^m)^(1/n).
Using the property (a^m)^n = a^(m * n), we can rewrite (a^m)^(1/n) as a^(m * 1/n), which simplifies to a^(m/n).
Therefore, we have now simplified the right-hand side (RHS) of the equation to a^(m/n).
Now that the LHS and RHS of the equation are equal, we have proved that a^(m/n) = n√(a^m).
By following the steps outlined above, we have shown the proof for the given equation.