Algebra question simplify

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qqrqq962

Mathematics

Description

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

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Explanation & Answer

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.


Anonymous
I was having a hard time with this subject, and this was a great help.

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