You can put this solution on YOUR website!
30 is not the 7th power of any number one can find manually. Nor does it have any 7th power factors (other than 1). So we cannot simplify this expression manually either.
But most calculators can find a decimal approximation for this. All we really need is a button for exponentiation. The button looks like "^" on many calculators. On some calculators the exponentiation button looks like .
The reason an exponentiation button will help is that
is the same as
So all we have to do is get your calculator to raise 30 to the 1/7 power. If your calculator has parentheses buttons, too, then you can literally type:
30^(1/7)
If your calculator does not have buttons for parentheses, then you have to get a decimal for 1/7 first. 1/7 is approximately 0.142857143. So you would type
30^0.142857143
P.S. In response to the question in your email...
1) You obviously have access to a computer. Look on the computer for a calculator program. Most computers have such a program. (If you use Windows you may find it in the Accessories folder.) The program may have the buttons you need to raise numbers to powers.
2) Unless your calculator only cost less than about $5, I am truly amazed that your calculator has no way to raise numbers to powers. You may want to double check. Maybe it's a "shift" or "2nd" function key. If you have the manual/instructions for the calculator, look in there for exponents, powers or exponentiation.
3) If your calculator has buttons for "log" and "log-1" then there is still a way:
3a) Use your calculator to find log(30)
3b) Divide the log(30) by 7
3c) Find log of the result from the previous step.
However, if your calculator really has no way to raise numbers to powers, it is unlikely to have buttons for "log" and "log-1"!?
4) A table of logarithms can help. Your Math book may have one in the back. (They used to be popular before calculators with logarithm keys became so inexpensive.) If you find a table of logarithms...
4a) Look up the log of 3
4b) Add 1 to the log of 3
4c) Divide that result by 7
4d) Look up the number whose logarithm is the result from 4c.
5) It looks like you are out of luck if none of the above help and you are unable to buy a calculator with these keys.
(