# Algebra

1. Express in terms of i:

-sqrt(-297)

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

8-1/3ax-7/8z^8

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

sqrt(20)k^7q^8

4. Simplify:

(-3a^2)^3

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

(2xy)^(-3)

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 Preview

Dear student, please refer to the attachment for the solutions. Thank You.

1. Express in terms of i.

-√-297

Solution: -√297i

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

8-1/3ax-7/8z8

Solution: 8-1/3ax- 7/(8z^8 )

(The problem is not clearly written. Please send a message re-writing the problem, so that I can update the solution).

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

√20k^7q^8

Solution: √20k^7 q^8 = 2k^3 q^4√5k

4. Simplify. ...

#### 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.