Algebra question simplify

Algebra
Tutor: None Selected Time limit: 1 Day

Simplify the following expressions and write them with positive exponents. 


a) x 2 x 3

b) a -2 a -3

c) a 5 / a 2

d) a -3 / a 7

e) (x 2) 3

f) (x -2) 5

g) (x 2 y 3) 3

h) (x -2 y 3) 8
Jul 26th, 2015

Thank you for the opportunity to help you with your question!

Here, we need to use the power rule, the quotient rule, and the product rule of exponents.

Power rule: (x^a)^b = x^(a*b)

Quotient rule: x^a / x^b = x^(a-b)

Product rule: x^a * x^b = x^(a+b)

a) x^2*x^3 = x^(2+3) = x^5

b) a^-2*a^-3 = a^(-2+ -3) = a^-5 = 1/a^5

c) a^5 / a^2 = a^(5-2) = a^3

d) a^-3 / a^7 = a^(-3-7) = a^-10 = 1/a^10

e) (x^2)^3 = x^(2*3) = x^6

f) (x^-2)^5 = x^(-2*5) = x^-10 = 1/x^10

g) (x^2*y^3)^3 = (x^2)^3 * (y^3)^3 = x^(2*3) * y^(3*3) = x^6*y^9

h) (x^-2*y^3)^8 = (x^-2)^8 * (y^3)^8 = x^(-2*8)*y^(3*8) = x^-16*y^24 = y^24 / x^16
Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 26th, 2015

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