SOLUTION: (1/243)^-3/5

Question 274380: (1/243)^-3/5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Until you get comfortable with exponents, a "trick" you can use to make simplifying expressions like this easier is to factor the exponent into "pieces".

can be factored into . And since multiplication is commutative we can order the factors any way we choose. I will choose: for reasons you will soon see. (Note: The simplification can be done using any order. The order I chose makes the problem a little easier as I hope you'll see.)

Rewriting the exponent in factored form we get:

Now I'll use the power of a power rule for exponents, , to rewrite this as powers of powers:

Now we can apply the exponents, from the inside out. Since -1 as an exponent means reciprocal the inner expression simplifies to:

As you can see, the fraction is gone! This makes the rest of the problem simpler. And this is exactly why I chose to put the -1 factor of the exponent first: To get rid of the fraction ASAP.

Next we'll apply the 1/5 exponent. 1/5 as an exponent means 5th root. And since , the 5th root of 243 is 3. So now we have:

The 243 is now a 3, a much smaller number which makes the remainder easier. And this is why I put the 1/5 factor second. I knew that the 5th root of any number over 1 is a much smaller number.

is 27. So your original expression simplifies down to 27.
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