Question 274380
{{{(1/243)^(-3/5)}}}
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".<br>
{{{-3/5}}} can be factored into {{{-1*3*(1/5)}}}. And since multiplication is commutative we can order the factors any way we choose. I will choose: {{{-1*(1/5)*3}}} 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.)<br>
Rewriting the exponent in factored form we get:
{{{(1/243)^(-1*(1/5)*3)}}}
Now I'll use the power of a power rule for exponents, {{{a^(p*q) = (a^p)^q}}}, to rewrite this as powers of powers:
{{{(((1/243)^(-1))^(1/5))^3)}}}
Now we can apply the exponents, from the inside out. Since -1 as an exponent means reciprocal the inner expression simplifies to:
{{{(243^(1/5))^3)}}}
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.<br>
Next we'll apply the 1/5 exponent. 1/5 as an exponent means 5th root. And since {{{243 = 3^5}}}, the 5th root of 243 is 3. So now we have:
{{{3^3}}}
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.<br>
{{{3^3}}} is 27. So your original expression simplifies down to 27.