Honors Algebra II: 5.1, 6.1, 6.2, and 6.6 Review

Simplify using the properties of exponents: (-4a²d⁵)³

-64a⁸d¹⁵

Simplify the expression using radicals and positive exponents: z^-⁵/³

1 / ³√z⁵

Simplify the expression involving scientific notation: (4 x 10⁵)(3.1 x 10^-7)

1.24 x 10^-1

Simplify the expression involving scientific notation: The United States consumes 1,500 water bottles every second. How many water bottles does the US consume in one day? State your answer using scientific notation.

1.296 x 10⁸ water bottles daily

Simplify the expression involving scientific notation: (4.3 x 10⁴)²

1.849 x 10⁹

Evaluate the expression without a calculator: (6)-²

1/36

Identify the simplest form of this expression: (x^-2)/(x⁹)

1/x¹¹

Identify the simplest form of this expression: (x⁹)^-2

1/x¹⁸

Identify the simplest form of this expression: (x²)(x^-9)

1/x⁷

Simplify using the properties of exponents: (4z⁶y²/x)²

16z¹²y⁴/x²

Simplify the expression: (³√4x³y⁵)(³√12y²)

2xy²(³√6y)

Simplify the expression involving scientific notation: 32.7 x 10⁵

3.27 x 10⁶

Simplify the expression: ⁴√81x⁴

3x

Simplify using the properties of exponents: (6g(^-2)h³)(7h⁴g(^-5))

42h⁷/g⁷

Simplify using the properties of exponents: ³√375 / ³√3

5

Simplify the expression involving scientific notation: 0.625 x 10^-4

6.25 x 10^-5

Evaluate the expression without a calculator: (√25)⁴

625

Simplify the expression involving scientific notation: (4.8 x 10⁶) / (6 x 10³)

8 x 10⁴

Solve the equation: (x + 7)⁴ = 50

x = -4.34 and -9.66

Solve the equation: (⁹√x - 8) = (⁹√ 3x + 4)

x = -6

Solve the equation: 4( x + 2 )^³/² = 32

x = 2

Solve the equation: 6x⁵ = -192

x = 2

Solve the equation: 3x³ = 81

x = 3

Solve the equation: ³√x-3 = 3

x = 30

Solve the equation: (⁴√3x + 4) - 11 = -9

x = 4

Solve the equation: -4x⁴ = -324

x = ±3

Solve the equation: (x^⁴/⁵) + 6 = 22

x = ±32

Solve the equation: x⁶ - 34 = 181

x ≈ ±2.45

Simplify the expression: x^¼ • x^⅓

x^¹/¹²

Rewrite the expression using rational exponents: √x

x^½

Rewrite the expression using rational exponents: ⁶√x⁸

x^⁴/³

Simplify using the properties of exponents: ⁵√ x¹⁰ / y⁵

x² / y

Simplify the expression: (√x²yz³)(x³z⁵)

x²z⁴√yx

Simplify the expression: ³√ x³ / y⁴

x³(√y²) / y²

Identify the simplest form of this expression: x²x⁹

x¹¹

Identify the simplest form of this expression: (x²)⁹

x¹⁸

Identify the simplest form of this expression: (x^-2)(x⁹)

x⁷

Simplify the expression: (y⁴)^¹/⁶

y^⅔

Simplify the expression: ⁴√12x²y⁶z¹²

yz³(⁴√12x²y²)

Rewrite the expression using rational exponents: (⁴√z)³

z^¾

Evaluate the expression without a calculator: 16^-⁷/⁴

±1/128

Evaluate the expression without a calculator: 49^½

±7

Simplify the expression using radicals and positive exponents: y^²/⁵

⁵√y²

Simplify the expression using radicals and positive exponents: x^⁶/⁷

⁷√x⁶