21. Simplify using exponent laws then evaluate when x=1 and y=-5 No decimal answers. a)x^2y^12x^5y^-9 b) (2x^5y^2)^2 c) (x^14y^7)/(x^12)y^(5)

## Step 1: Simplify Part (a)<br />### Combine the $x$ terms and the $y$ terms separately by adding the exponents. $x^{2}y^{12}x^{5}y^{-9} = x^{2+5}y^{12+(-9)} = x^7y^3$. Substitute $x=1$ and $y=-5$: $(1)^7(-5)^3 = 1 \cdot (-125) = -125$.<br /><br />## Step 2: Simplify Part (b)<br />### Distribute the exponent to each term inside the parentheses by multiplying the exponents. $(2x^{5}y^{2})^{2} = 2^2x^{5 \cdot 2}y^{2 \cdot 2} = 4x^{10}y^{4}$. Substitute $x=1$ and $y=-5$: $4(1)^{10}(-5)^{4} = 4 \cdot 1 \cdot 625 = 2500$.<br /><br />## Step 3: Simplify Part (c)<br />### Divide the $x$ terms and the $y$ terms separately by subtracting the exponents of the denominator from the exponents of the numerator. $\frac {x^{14}y^{7}}{x^{12}y^{5}} = x^{14-12}y^{7-5} = x^2y^2$. Substitute $x=1$ and $y=-5$: $(1)^2(-5)^2 = 1 \cdot 25 = 25$.