How do you simplify each expression using positive exponents #(x^-2y^-4x^3)^-2 #?

1 Answer
Zack M.
Jan 7, 2016

#y^8/x^2#

Explanation:

We can use exponent rules to simplify this expression. Taking a look at the original function;

#(x^-2y^-4x^3)^-2#

We can see that there are two #x# terms inside of the parenthesis. Lets combine those first. If we multiply two terms with exponents, the exponents add, in other words;

#x^a xx x^b = x^(a+b)#

Applying this to our case, we get;

#(x^((3-2))y^-4)^-2#

#(x^1y^-4)^-2#

Now lets take a look at the exponent outside the parenthesis. Whenever we raise an exponent term to an exponent, we multiply the exponents.

#(x^a)^b = x^((a)(b))#

In our case, raising both the #x# term and the #y# term to #-2# we get;

#x^((-2)(1))y^((-2)(-4))#

#x^-2y^8#

Now we have one negative exponent and one positive exponent. We need to convert the #x# term to a positive exponent. To do that we will invert the term.

#x^-a = 1/x^a#

So to get rid of the #-# we will move the #x# term to the denominator.

#y^8/x^2#

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