The exponent is -2/3.
The negative sign means that the problem belongs in the denominator with a positive exponent.
(-125) ^ (-2/3) = 1 / [ (-125) ^ (2/3) ]
An exponent of 2/3:
--- the numerator of 2 means that you need to square the number
--- the denominator of 3 means that you need to find the cube root of the number
and you can do these two operations in eiter order.
If you square first, you get: 1 / [ (15625) ^ (1/3) ]
Now, finding the cube root: 1 / ( 25) = 1 / 25.
If you find the cube root first, you get: 1 / [ (-5) ^ 2 ]
Now, squaring: 1 / (25) = 1 / 25.
Generally, if you find the root first, you will be working with smaller numbers.
The exponent is -2/3.
The negative sign means that the problem belongs in the denominator with a positive exponent.
(-125) ^ (-2/3) = 1 / [ (-125) ^ (2/3) ]
An exponent of 2/3:
--- the numerator of 2 means that you need to square the number
--- the denominator of 3 means that you need to find the cube root of the number
and you can do these two operations in eiter order.
If you square first, you get: 1 / [ (15625) ^ (1/3) ]
Now, finding the cube root: 1 / ( 25) = 1 / 25.
If you find the cube root first, you get: 1 / [ (-5) ^ 2 ]
Now, squaring: 1 / (25) = 1 / 25.
Generally, if you find the root first, you will be working with smaller numbers.