49 to the 2/3 power I have put this in many calculators and have gotten different answers?

49^(2/3)

2 Answers
Jan 28, 2018

49^(2/3)=root(3)(2401)~~13.4

Explanation:

49^(2/3)=(7^2)^(2/3)
(7^2)^(2/3)=7^(2xx2/3)
7^(2xx2/3)=7^(4/3)
7^(4/3)=root(3)(2401)
root(3)(2401)~~13.4

Feb 1, 2018

Ensure that you indicate to the calculator:

root3(49^2) = root3(2401) = 13.3905

(root3 49)^2 = (3.6593)^2 = 13.3905

Explanation:

You need to be sure to tell the calculator exactly what you mean.

This can be done using brackets, or by working out one part first, pressing the equal sign, and then doing the second part.

Some calculators have an ANS key which allows you to use the previous answer in the next calculation. On simpler calculators you might need to use the Memory function.

Simply typing in: "49^2" div 3" will be understood as 49^2/3 because a power is calculated before a division.

This will give the answer 800.3333333

You might inadvertently tell the calculator (49/3)^2
This will give the answer 266.77777778

However, if you use brackets correctly you will be showing that the base of 49 is to be raised to an index which is a fraction.

49"^"(2div3) will be understood as 49^(2/3)

This actually means: root3(49^2) or (root3 49)^2

Both methods will give the same answer.

root3(49^2) = root3(2401) = 13.3905

(root3 49)^2 = (3.6593)^2 = 13.3905

YOu can also do two steps:

2div 3 = 0.666666666...

49" ^ ANS" = 13.3905

Note that the answer is irrational and has been rounded to 4 decimal places.

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If the question had been 49^(3/2) we would have had a rational answer:

49^(3/2) = (sqrt49)^3 = 7^3 = 343

or

sqrt(49^3) = sqrt117649 = 343