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Polynomials and Decimals

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How do you

8) Simplify ((-8a^-1b^-3)/(2a^3b))^-2

9) Simplify (3x^4)^2(4x^-5)^-1 divided by 12x^-6

10) Simplify (5x^2y^4)^2(-3x^-4y^-1)^3

11) Simplify -24a^3b^5 + 36a^2b^2 - 12ab^2 divided by -4ab

12) How do you Write these in standard (decimal) notation:

a) 2.45 X 10^3
b) 3.342 X 10^-4
c) 5.3 X 10^6

Write these in scientific notation:

d) 344232542124
e) .0003234
f) .078

13) Simplify SR(45x^23)

14) Simplify 4th root of (x^5 divided by 16y^15)

15) Simplify (x^1/4 y^1/2)^2(x^2y^3)^1/2

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Solution Preview

how do you

8) Simplify ((-8a^-1b^-3)/(2a^3b))^-2

First of all, a negative exponent flips the whole thing upside down, and the exponent can be distributed to both the top and bottom.
(2a3b)2 = 2a6b2 = 2a6b2*-8a2b6= -16a8b8
(-8a-1b-3)2 -8a-2b-6


9) Simplify (3x^4)^2(4x^-5)^-1 divided by 12x^-6

(3x4)2 (4x-5)-1 = ...

Solution Summary

This shows how to simplify and work with polynomials and also how to convert decimals to scientific notation.