Chapters

## Exercise 1

Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

13x³

25x^{−3 }

33x + 1

4

5

6

7

## Exercise 2

Simplify:

12x²y³z + 3x²y³z

22x³ − 5x³ =

33x^{4} − 2x^{4} + 7x^{4} =

42 a²bc³ − 5a²bc³ + 3a²bc³ − 2 a²bc³ =

## Exercise 3

Solve:

1(2x³) · (5x³) =

2(12x³) · (4x) =

35 · (2x²y³z) =

4(5x²y³z) · (2y²z²) =

5(18x³y²z^{5}) · (6x³yz²) =

6(−2x³) · (−5x) · (−3x²) =

## Exercise 4

Solve:

1(12x³) : (4x) =

2(18x^{6}y²z^{5}) : (6x³yz²) =

3(36x³y^{7}z^{4}) : (12x²y²) =

4

5

6

## Exercise 5

Solve:

1(2x³)³ =

2(−3x²)³ =

3

## Solution of exercise

## Solution of exercise 1

Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

13x³

Degree: 3, coefficient: 3

2 5x^{−3 }

It is not a monomial because the exponent is not a natural number.

33x + 1

It is not a monomial because there is an addition.

4

Degree: 1, coefficient:

5

Degree: 4, coefficient:

6

It is not a monomial because it does not have a natural exponent.

7

It is not a monomial because the literal part is within a root.

## Solution of exercise 2

Simplify:

12x²y³z + 3x²y³z = 5x²y³z

22x³ − 5x³ = −3x³

33x^{4} − 2x^{4} + 7x^{4} = 8x^{4}

42a²bc³ − 5a²bc³ + 3a²bc³ − 2a²bc³ = −2a²bc³

## Solution of exercise 3

Solve:

1(2x³) · (5x³) = 10x^{6}

2(12x³) · (4x) = 48x^{4}

35 · (2x² y³z) = 10x²y³z

4(5x²y³z) · (2 y²z²) = 10x²y^{5}z³

5(18x³y²z^{5}) · (6x³yz²) = 108x^{6}y³z^{7}

6(−2x³) · (−5x) · (−3x²) = −30x^{6}

## Solution of exercise 4

Solve:

1(12x³) : (4x) = 3x²

2(18x^{6}y²z^{5}) : (6x³yz² ) = 3x³yz³

3(36x³y^{7}z^{4}) : (12x²y²) = 3xy^{5}z^{4}

4

5 4x³y + 3x²y² − 8x^{8}

6

## Solution of exercise 5

Solve:

1(2x³)³ = 2³** · ** (x³)³ = 8x^{9}

2(-3x²)³ = (-3)³** · **(x³)² = −27x^{6}

3

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