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1. Express in terms of i:

2. Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero.

3. Simplify. Assume that no radicals were formed by raising negative numbers to even powers.

4. Simplify:

5. Simplify. Do not use negative exponents in your answer.


6. Add.
3x^8 + 8x^7 + 6x^6 - 4
5x^8 + 2x^7 + 6x^6 - 8

7. Find the degree of the given polynomial.
-4y^8 - 3x^7z + 4xz^7

8. Multiply.
(m^3n - 9)(m^3n - 5)

9. Perform the indicated operation.
(42k^3 + 12k^2 + 18k) ÷ (6k)

10. Solve the problem. If necessary, round to the nearest tenth.
A car dealer advertised a big sale by stretching a string of banners from the top of the building to the edge of the driveway. If the building is 26 m high and the driveway is 43 m from the building, how long is the string of banners?

11. Factor the expression into a product of two binomials.
5x(3x - 5) + 2(3x - 5)

12. Factor completely. If the polynomial is prime, state this.
75x^2 - 3

13. Factor completely. If the polynomial is prime, state this.
48x^2 + 40xy - 48y^2

14. Factor by grouping, if possible.
x^3 + 3x^2 + 8x + 24

Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problem and provides students with a clear perspective of the underlying concepts.