need help again!!!!!
Simplify the expression. Use only positive exponents.
8x^2 y^-2 . (4xy^2)^-1
__________ ____________
x^-2y x^2y
i'm sorry i can't read your question that well. use "/" sign for fractions and "*" sign for multiplication please.
2x2
No problem! I can help you with that. To simplify the expression
(8x^2 y^-2 * (4xy^2)^-1) / (x^-2y * x^2y), you can follow these steps:
Step 1: Simplify each term inside the parentheses first.
a) Simplify the term 4xy^2 to its positive exponent form:
(4xy^2)^-1 = 1 / (4xy^2)^1 = 1 / 4xy^2
Step 2: Apply the exponent rules:
a) When dividing exponential terms with the same base, subtract the exponents:
x^2 / x^-2 = x^(2 - (-2)) = x^4
b) When dividing exponential terms with the same base, subtract the exponents:
y^(-2) / y = y^(-2 - 1) = y^-3 = 1 / y^3
c) When multiplying exponential terms with the same base, add the exponents:
x^2 * x^4 = x^(2 + 4) = x^6
d) y^-3 * y^2 = y^(-3 + 2) = y^-1 = 1 / y
Step 3: Substitute the simplified terms into the expression:
(8x^6 * (1 / 4xy^2)) / (1 / y * x^2y)
Step 4: Simplify further by multiplying the numerator and denominator by the reciprocal of the denominator:
(8x^6 * (1 / 4xy^2)) * (y * x^2y / 1)
Step 5: Simplify by canceling out common factors and multiplying:
8x^6 * (1 / 4xy^2) * y * x^2y
Step 6: Multiply the coefficients and combine the variables:
= (8 * 1 / 4) * (x^6 / x) * (y / y^2) * (x^2y)
= 2 * x^(6 - 1) * y^(1 - 2) * x^(2 + 1) * y
= 2x^5 / y * x^3 * y
= 2x^5y / y * x^3
= 2x^5 * x^3
= 2x^8
So, the simplified expression is 2x^8.