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Help student to understand basic algebra equations & concept

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Please help with my review class. This is supposed to be elementary Algebra, but I am having a hard time understanding it. Please help me to understand better and if are able to help please explain so that I can understand it.
Thank you.

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Solution Summary

Assist the student by working common examples in solving and simplifying basic algebra equations. Examples include problems involving fractions, polynomials, etc. Addition, subtraction, product, and quotient of polynomial and binomials. Product rule for exponents. Power of a power rule. Power of a Product Rule. Power of a Quotient Rule. Negative and Integral Exponents. The Additive Inverse of a Polynomial. FOIL Method. Multiply Binomials Quickly. Square of Sum or Difference. Product of a sum and a difference of terms. Scientific notation, rounding, and calculator operations on scientific notation.

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Solutions in the attached file for the following problems:
1) Product rule for exponents
a. -6st * 9st = -54s2t2
b. 8s^2t^13 / (-2st^5) = 4st8

2) Power of a Power Rule
a. -3x(x^5)^2 / 6 x^3 (x^2) ^ 4 = -1/2

3) Power of a Product Rule
(a^3b^4c^5)^4 / (a^2b^3c^4)^2 = a8b10c12

4) Power of a Quotient Rule
( -2a^2/b^3)^4 = 16a8 /b12

5) Negative Integral Exponents
a. 5^-2 / 10^-2 = 6
b. 3a^-3 / b^-9 = 3 (b3/a )3
c. (5/2)^-3 = 8 / 125
d. 8t^-3 / (-2t^-5) = -4 t2
e. ((2s^-1*t^3) / (6s^2t^-4) )^ -3 = 27s9t-21

6) Addition and Subtraction of Polynomials
a. (w^5 - w^3) - (-w^4 + w^2) = W5 + W4 -W3 -W2
b. (9 - 3y - ...

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