SOLUTION: Explain how you use the 5 rules of exponents to simplify the following expressions. Do not leave any negative exponents in your answer.: a. (x^10 · y^3)/(x^4 · y^5) b. [(p^4 ·

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Explain how you use the 5 rules of exponents to simplify the following expressions. Do not leave any negative exponents in your answer.: a. (x^10 · y^3)/(x^4 · y^5) b. [(p^4 ·       Log On


   

Question 22386: Explain how you use the 5 rules of exponents to simplify the following expressions. Do not leave any negative exponents in your answer.:
a. (x^10 · y^3)/(x^4 · y^5)
b. [(p^4 · q^5)/(r^3)]^2
c. (108r^2 · y)/(9r^3 · y^2)
d. (3x^2 · y^2) · (-5x · y^4)^2

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
a. %28x%5E10+%2A+y%5E3%29%2F%28x%5E4+%2A+y%5E5%29+
When you divide with the same base number, you subtract exponents.
x%5E6%2Ay%5E%28-2%29

When you have a negative exponent such as y%5E%28-2%29 it becomes a fraction whose numerator is 1, and the denominator is y%5E2 or 1%2F%28y%5E2%29+
x%5E6+%2A%281%2F%28y%5E2%29%29+
%28x%5E6%29%2F%28y%5E2%29

b. %28%28p%5E4+%2A+q%5E5%29%2F%28r%5E3%29%29%5E2+
When you raise a power to a power, you multiply the exponents:
+%28p%5E8+%2Aq%5E10%29%2F%28r%5E6%29+

c. +%28108r%5E2+%2A+y%29%2F%289r%5E3+%2A+y%5E2%29+
Rewrite the fraction into three fractions:
%28108%2F9%29%2A%28r%5E2%2Fr%5E3%29%2A%28y%2F%28y%5E2%29%29+
%2812%29%2A%281%2Fr%29%2A+%281%2Fy%29+
12%2F%28ry%29

d. %283x%5E2+%2A+y%5E2%29+%2A+%28-5x+%2A+y%5E4%29%5E2+
Square everything in the second parentheses:
%283x%5E2+%2Ay%5E2%29+%2A%2825%2Ax%5E2%2Ay%5E8%29+
When you multiply with the same base number, you add exponents:
75x%5E4y%5E10+

R^2 at SCC