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Basic algebraic expressions

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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)

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Solution Summary

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

Solution Preview

Please refer attached file for better clarity and understanding of expressions.

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 ...

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  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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