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Simplifying Exponents and Polynomials

Simplify. All variables represent nonzero real numbers.

1.) -5y^4 (y^5)^2
15y^7 (y^2)^3

2.) 3y^8 This whole problem is ^4
2zy^2

3.) 3^3 This whole problem is ^4
3

Simplify.

4.) 4 This whole problem is ^-2
3

5.) w^-4
w^6

6.) 2s^-1 t^-3 This whole problem is ^-3
6s^2 t^-4

Write each number in standard notation.

7.) 9.3x10^-5

8.) 8x10^6

Perform the computations.Write answers in scientific notation.

9.) 9x10^-4
3x10^-6

Evaluate each polynomial as indicated.

10.) Evaluate: -2x^4-3x^2+5x-9 for x=12.

Perform the indicated operation.

11.) (w^2-2w+1) + (2w-5+w^2)

12.) (4-5y+y^3) - (2-3y+y^2)

Find each product.

13.) -12sq * 3s

14.) (3c^2d - d^3 +1) 8cd^2

Perform the indicated operation.

15.) (5x-6) (5x-6)

Use FOIL to find each product.

16.) (11x+3y) (x+4y)

17.) (5y^3w^2+z) (2y^3w^2+3z)

18.) (3h-5) (3h+5)

Find each product.

19.) (3y^2+1) (3y^2-1)

20.) (3z^4-8)^2

21.) 2 y - 1 This whole problem is ^2
3 2

Find each quotient. Try to write only the answer.

22.) b^19
b^12

23.) -12z^10 y^2
-2z^4 y^2

Find the quotients.

24.) 5y-10
-5

Write each expression in the form
quotient + remainder.
Divisor

25.) 2x^2+4
2x

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Solution Summary

This solution explains through a variety of problems how to simplify exponents and polynomials.

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