simplify the expression. Use only positive exponents.
8x^2y^-2/x^-2y * (4xy^2)^-1/x^2y
Something does not seem right in your terms.
Are you saying that 8x is being taken to the 2y power and that all this being taken to the -2x power?
Please clarify your terms, and we will do our best to help you — but not do the work for you.
I hope this helps. Thanks for asking.
I apologize for the confusion. Let's break down the expression step by step and simplify it:
Given expression: 8x^2y^(-2)/x^(-2)y * (4xy^2)^(-1)/x^2y
Step 1: Simplify the exponents of the variables inside the parentheses.
(4xy^2)^(-1) can be written as 1/(4xy^2)^1.
Our expression now becomes: 8x^2y^(-2)/x^(-2)y * 1/(4xy^2)^1/x^2y
Step 2: Apply the exponent rule: x^(-n) = 1/x^n
Rewrite the denominator x^(-2) as 1/x^2.
Our expression becomes: 8x^2y^(-2)*(1/x^2)y * 1/(4xy^2)^1/x^2y
Step 3: Simplify the expression inside the parentheses (4xy^2)^1:
(4xy^2)^1 = 4xy^2
Our expression becomes: 8x^2y^(-2)*(1/x^2)y * 1/(4xy^2)/x^2y
Step 4: Combine the fractions by multiplying the numerators and denominators.
Multiply the numerator: 8x^2 * (1/x^2) = 8x^2/x^2 = 8
Multiply the denominator: y^(-2) * y = y^(-2+1) = y^(-1) = 1/y
Our expression becomes: 8 * (1/y) * 1/(4xy^2)/x^2y
Step 5: Simplify the expression 1/y * 1/(4xy^2)/x^2y
Divide the fractions: (1/y) * (x^2y/4xy^2) = (xy)/(4xy^2) = (x/x)(y/4y^2) = 1/4y
Our expression becomes: 8 * (1/4y)
Step 6: Simplify the expression 8 * (1/4y)
Multiply the whole number: 8 * (1/4) = 8/4 = 2
Our expression simplifies to: 2/y
Therefore, the simplified expression is 2/y, where y is a positive number.