Algebra 1 Semester 2 Final Review - Part 1 (Systems & Exponents)

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15x²y⁷

(-15xy⁴)(-xy³)

-(3x)/y³

(-21x⁵y²)/(7x⁴y⁵)

-27x³

(-3x)³

-8x⁵y⁴

(-4x²y)²(-½xy²)

1

(-99)⁰

-x⁴y³z

(-xy)³(xz)

0.4x⁴y⁶

(0.2x²y³)²

0.064x⁹

(0.4x³)³

x⁴/3

(12x⁵)/(36x)

3x⁵y²

(15x⁶y⁻⁹)/(5xy⁻¹¹)

9/4

(2/3)⁻²

4x⁶y⁸

(2x³y⁴)²

16/9

(3/4)⁻²

4/3

(3/4)⁻¹

-4x²yz³

(32x³y²z⁵)/(-8xyz²)

9x²y⁴

(3xy²)²

25/16

(4/5)⁻²

-(8x⁵y²)/z

(48x⁶y⁷z⁵)/(-6xy⁵z⁶)

1

(4x³/2x⁵)⁰

-8x⁸y

(4x³y)(-2x⁵)

(16x¹⁴)/(49y⁴)

(4x⁷/7y²)²

6

(6⁵)/(6⁴)

3x

(9x⁷)/(3x⁶)

9⁴

(9¹²)/(9⁸)

y²/x²

(x/y)⁻²

y/x

(x/y)⁻¹

x⁷

(x²/x⁻⁵)

y⁶/x⁶

(x²/y²)⁻³

x⁹

(x³/x⁻⁶)

y³/x³

(x³/y³)⁻¹

(1)/(y²)

(x³y²)/(x³y⁴)

(x⁴)/(x²)

(x⁴y³)/(x⁴y)

(x⁷y²)/(x⁴y²)

1/x⁷

(x⁻³)/(x⁴)

1/x⁹

(x⁻⁴)/(x⁵)

(y⁴z²)/x⁵

(x⁻⁵y⁴)/(z⁻²)

¼x²y⁶

(½xy³)²

(6, 4)

-x + 3y = 6, x + 3y = 18

(5, 6)

-x + y = 1, x + y = 11

1

100⁰

(-1, 2)

2m + 3n = 4, -m + 2n = 5

(2.5, 0)

2x + 2y = 5, 4x - 4y = 10

(-3, 4)

2x + 3y = 6, x + 2y = 5

(-3, -5)

2x - 3y = 9, 5x + 3y = -30

(1, 1)

3a - b = 2, a + 2b = 3

(-3, 7)

3x + 4y = 19, 3x + 6y = 33

(-5, -4)

3x - 2y = -7, 2x - 5y = 10

infinitely many solutions

3x - 4y = -4, 6x - 8y = -8

(-1, -2)

3x - y = -1, -3x - y = 5

(10, 4)

3x - y = 26, -2x - y = -24

(-0.5, 2)

4x - 3y = -8, 2x + 2y = 3

(4, -2)

4x - 3y = 22, 2x - y = 10

(2, -1)

4x - y = 9, 5x + 2y = 8

1/(4⁴) or 1/256

4⁻⁴

(-1, 1)

5x - y = -6, -x + y = 2

1/(8²) or 1/64

8⁻²

No; this is the quotient, not the product, of two variables.

Is it a monomial? (21a²)/7b

Yes; this is the product of the number 1/2 and two variables.

Is it a monomial? (b³c²)/2

Yes; 11 is a real number and an example of a constant.

Is it a monomial? 11

No; this is the sum of two monomials.

Is it a monomial? 2a + 3b

No; this is the difference, not the product, of two variables.

Is it a monomial? a - b

Yes; this is the product of two variables.

Is it a monomial? j³k

No; this is the quotient, not the product, of two variables.

Is it a monomial? p²/r²

Yes; single variables are monomials.

Is it a monomial? y

8x⁵y²

Simplify (-2x⁴y)(-4xy)

-15x⁶y

Simplify (-5x²y)(3x⁴)

-15x¹¹

Simplify (-5x³)(3x⁸)

36x²

Simplify (-6x)²

10⁶ or 1,000,000

Simplify (10²)³

8a⁴b⁴c⁴

Simplify (2ab²c²)(4a³b²c²)

6x⁷

Simplify (2x²)(3x⁵)

-6x³y⁴

Simplify (3xy⁴)(-2x²)

12x⁴y⁸

Simplify (4xy³)(3x³y⁵)

20x⁹

Simplify (5x⁷)(4x²)

7x⁷y⁵

Simplify (7x⁵y²)(x²y³)

a⁴b⁴

Simplify (ab²)(a³b²)

a⁴b⁸

Simplify (a²b⁴)(a²b⁴)

x³⁶

Simplify (x³)¹²

y³z³

Simplify (y²z)(yz²)

y⁵z³

Simplify (y²z²)(y³z)

x¹⁰

Simplify x(x²)(x⁷)

x¹¹

Simplify x²(x³)(x⁶)

y = -2/3x + 2 and y = -2/3x - 2

What are the equations for this system?

y = -3 and y = x - 1

What are the equations for this system?

y = -3/2x + 3 and y = -3/2x + 1

What are the equations for this system?

y = -3/2x and y = -1/2x

What are the equations for this system?

y = -4x + 3 and y = -4x - 2

What are the equations for this system?

y = 1/2x - 2 and x - 2y = 4

What are the equations for this system?

y = 2x + 1 and 2x - y = -1

What are the equations for this system?

y = 2x + 1 and y = -1/2x + 4

What are the equations for this system?

y = 3x - 4 and y = -x

What are the equations for this system?

infinitely many solutions

What is the SOLUTION to the system?

no solution

What is the SOLUTION to the system?

one solution; (-2, -3)

What is the SOLUTION to the system?

one solution; (0, 0)

What is the SOLUTION to the system?

one solution; (1, -1)

What is the SOLUTION to the system?

one solution; (2, 3)

What is the SOLUTION to the system?

x⁸

[(x²)²]²

x²⁴

[(x²)³]⁴

no solution

solve by substitution: 2x + y = 5 and 2x + y = 7

infinitely many solutions

solve by substitution: 2x + y = 7 and y = -2x + 7

(6, -3)

solve by substitution: 2x - 3y = 21 and y = 3 - x

infinitely many solutions

solve by substitution: 3x + y = 8 and y = -3x + 8

no solution

solve by substitution: x = -5y + 4 and 3x + 15y = -1

(2, -3)

solve by substitution: x = 2 and 2x + y = 1

(-6, 1)

solve by substitution: x = y - 7 and x = -8y + 2

(-2, -4)

solve by substitution: y = 2x and x + 3y = -14

(1, 2)

solve by substitution: y = 2x and x + y = 3

no solution

solve by substitution: y = 3 and y = 5

no solution

solve by substitution: y = 3x + 5 and y = 3x + 4

(-1, 5)

solve by substitution: y = 3x + 8 and 5x + 2y = 5

infinitely many solutions

solve by substitution: y = 3x - 2 and y = 3x - 2

(3, 9)

solve by substitution: y = 3x and 2x + y = 15

(-2, -9)

solve by substitution: y = 4x - 1 and y = 2x - 5

(1, 4)

solve by substitution: y = 4x and x + y = 5

no solution

solve by substitution: y = 5x - 1 and y = 5x + 2

infinitely many solutions

solve by substitution: y = 5x - 9 and y = 5x - 9

(2, 1)

solve by substitution: y = x - 1 and x + y = 3

(1, 0.2)

x + 10y = 3, 4x + 5y = 5

(-8, 0)

x + 4y = -8, x - 4y = -8

(11, 0)

x + 4y = 11, x - 6y = 11

no solution

x + y = 3, 2x + 2y = 4

infinitely many solutions

x + y = 3, 2x + 2y = 6

(2, 1)

x - y = 1, x + y = 3

(0, -4)

x - y = 4, 2x + y = -4

1/(x²)

x/(x³)

x²y³

x²y³z⁰

(x²y³)/(z⁴)

x²y³z⁻⁴

x²y⁰

(x²)/(y³)

x²y⁻³

(x²z⁴)/(y³)

x²y⁻³z⁴

(x³)/(y²)

x³y⁻²

1

x⁰

1/x²

x⁰(x⁴)(x⁻⁶)

1/(x²y³)

x⁻²y⁻³

1/x³

x⁻³

1/x⁴

x⁻⁴

1

y⁰


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