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(-125)^-2/3

 Oct 3, 2014

Best Answer 

 #1
avatar+23252 
+5

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.

 Oct 3, 2014
 #1
avatar+23252 
+5
Best Answer

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.

geno3141 Oct 3, 2014

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