Question

In regrads to the epression 9^2/3

Why is this not an equivilent statement to (3^2)^2/3

The reason i ask this question is because while working with exponents in two seperate problems it was handled two different ways.

In the problem 9^3/4 * 3^7/2 Over 27^3/2 and then continue on into the problem and it works fine

So why does it not work with the top problem



The book shows us chaging the 9 ^3/4 to (3^2)^3/4 and the 27^3/2 to (2^3)^3/2

Answer 1

it is an equivalent statement. my guess would b that u are using an online system and it wanted the exponent in the most reduced form. or u typed it in wrong

Answer 2

I have a question that goes along with this. I see why it is equivilent when you properly apply the order of operations it goes backwards, however how does the following eample work

My book tells us that using the powers to powers rule (2^3)^3 = us multiplying the exponets together and we get 2^9

Then my book goes on to tell us that when we want to use the same rule for fraction eponents as in 3^5/2 When can say that is = to( 3^1/2)^5

If we go by the powers to powers rule we would multiply 1/2 * 5

My point is why is the order of perations not used in this case. Why are we mulitplying the exponets instead of doingwhat is in the parenthatsis

Answer 3

order of operations is the technique we use to solve equations. what ur book is trying to teach u is how to write equivalent expressions not solve the equation. when following certain rules like ur powers rule we may write our equations in a way that is easier for us to solve.