Could someone please explain to me why this is true:
5^2/3x25^2/3=25 I understand problems like 5^4+5=5^5 is false, but it's simpler. I'm just not getting what makes the top problem true
You need to use parentheses in your problem
5^2/3x25^2/3=25
I have no idea what this means?
Is this your problem?
5^2/3 x 25^2/3 = 25
This does not equal 25.
For the above to be true you will have to write it s
(5^(2/3)) (25^(2/3))
= (5^(2/3))(5^(4/3))
= 5^(6/3)
= 5^2
= 25
thanks REINY. After seeing your post, the problem, as I typed without parentheses, is apparent. I don't know why I didn't see that! Parentheses are nice though.
To understand why the equation 5^(2/3) * 25^(2/3) equals 25, we need to break down the concept of fractional exponents and the properties of exponents.
Let's start with the basics. The fractional exponent represents a root. For example, when we have a fractional exponent of 2/3, it means we are taking the square root (2nd root) and then the cube root (3rd root) of the number.
In this equation, 5^(2/3) can be thought of as finding the cube root of 5 and then squaring the result. Similarly, 25^(2/3) means taking the cube root of 25 and then squaring the result.
First, let's calculate the cube root of 5. The cube root of a number can be approximated to 2 decimal places. So, the cube root of 5 is approximately 1.71.
Next, we square the cube root of 5, which gives us 1.71 * 1.71 = 2.9241 (rounded to 4 decimal places).
Now, let's calculate the cube root of 25. The cube root of 25 is 2, as 2 * 2 * 2 = 8, and 8 is the cube of 2.
Then, we square the cube root of 25, 2 * 2 = 4.
Finally, let's multiply the two results together: 2.9241 * 4 = 11.6964 (rounded to 4 decimal places).
As you can see, the value resulting from 5^(2/3) * 25^(2/3) is approximately 11.6964, not 25. Therefore, it seems there might be an error in the initial equation.
To summarize, the equation 5^(2/3) * 25^(2/3) does not equal 25. However, if there was a mistake in the equation or if further simplification has occurred that was not mentioned, please provide that information so that I can help explain it further.