Algebra 1 Semester 2 Final Review - Part 1 (Systems & Exponents)
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)
x²
(x⁴)/(x²)
y²
(x⁴y³)/(x⁴y)
x³
(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
x²
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
