Simplify the exponential expression. Assume the variables represent nonzero real numbers.
(2^-1 x^-5 y^-5)^-2 (2x^-2 y^4)^-2(4x^-2 y^4)^0
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(2x^-5 y^-5)^2
the line by the way means to divide. i have no idea how to solve :( All i know is the (4x^-2 y^4)^0 is equal to 1 and that kinda cancels itself out.
To simplify the given expression, let's break it down step by step.
Step 1: Simplify the exponents inside the parentheses using the power of a power rule:
(2^-1 x^-5 y^-5)^-2 = 2^(-1*-2) x^(-5*-2) y^(-5*-2) = 2^2 x^10 y^10
Step 2: Simplify the exponents inside the second set of parentheses:
(2x^-2 y^4)^-2 = 2^(-2*-2) x^(-2*-2) y^(4*-2) = 2^4 x^4 y^-8
Step 3: Simplify the exponent outside the second set of parentheses:
(4x^-2 y^4)^0 = 1
Step 4: Combine the simplified expressions from step 1, step 2, and step 3:
(2^2 x^10 y^10)(2^4 x^4 y^-8)(1) = 2^6 x^14 y^2 y^-8 = 64x^14 y^-6
Step 5: Simplify the expression (2x^-5 y^-5)^2 in the denominator:
(2x^-5 y^-5)^2 = 2^2 x^(-5*2) y^(-5*2) = 4x^-10 y^-10
Step 6: Divide the numerator expression by the denominator expression:
64x^14 y^-6 รท 4x^-10 y^-10 = 64/4 * x^(14-(-10)) * y^(-6-(-10)) = 16x^24 y^4
Therefore, the simplified expression is 16x^24 y^4.