How do you simplify the following and please show all work.
(-3x(-4 exponent)y(3 exponent)
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(2x(5 exponet) y(-2 exponent)
then the whole equation is in ()with a -2 exponent
bring the denominator x,y to the numerator and change the signs of the ex>3 * x3 =
x3 + 3=
x<supp>6</sponents. Then add exponents to like components (x, or y).
example:
x3 / x-3 =
x<supup>
To simplify the given expression, let's break it down step by step:
1. Use the rule of exponents that states when you have a negative exponent, you can move the term to the opposite side of the fraction as a positive exponent:
(-3x^(-4)y^(3)) / (2x^(5)y^(-2))^(-2)
2. Apply the negative exponent to each term inside the parentheses:
(-3x^(-4)y^(3)) / (2^(-2)x^(-5)y^(-2))
3. Simplify further by using the rule of exponents for negative exponents: Any term with a negative exponent can be rewritten as its reciprocal with a positive exponent:
(-3y^3) / (2^(-2) * x^(-5) * (1/y^2))
4. Simplify the expression inside the parentheses:
(-3y^3) / ((1/2^(2)) * (1/x^5) * (1/y^2))
5. Simplify the fraction by multiplying the numerator and denominator by the reciprocal of the denominator:
-3y^3 * (2^2 * x^5 * y^2) / 1
6. Simplify the expression in the numerator:
= -3 * 2^2 * x^5 * y^3 * y^2
= -12x^5y^(3+2)
= -12x^5y^(5)
So, the simplified form of the given expression is -12x^5y^5.