# Basic algebraic expressions

1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents

(12x^7y^9)/(36xy^7

2. Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression.

(-3x^6y)^3

3. Simply the following expression, and rewrite it in an equivalent form with positive exponents.

(-6x^-5)^(-2)

4. Add the polynomials, and simply the resulting expression

(-4x^2 -9x -8) + (-10x^2+5x-6)

5. Multiply the expressions, and simplify.

(-10x^-5y^-2) ? (-9x^-4y)

6. Short Answer: Convert this number to scientific notation:

496,700,000

7. Use scientific notation to divide the following two numbers. Express the answer using scientific notation; retain at least three decimal places.

8.16*10^5 / 1.03*10^2

8. Add the complex expressions, and simplify.

(1.9 - 7i) + (4.2 - 2.3i)

9. Short Answer: Simplify the following expression; express in terms of i

Sqrt(-36)

10. Simplify the following expression.

Sqrt(-24)sqrt(-81)

#### Solution Preview

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1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents

12x^7y9/36 xy^7

=(12/36)* x(7-1)* y(9-7)

=(1/3)* x6 y2

= (x6 y2)/3

2. Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression.

(-3x^6y)^3

=(-3)^(1*3)x^(6*3) y(1*3)

=-27 x^18 ...

#### Solution Summary

There are 10 problems. Each problem is solved by using basic algebra techniques.