Simplify the exponential expression 2⁴ × 2³ using properties of integer exponents.
Real Numbers And Exponents
Question · Easy
Slope: up or down? Pick fast
Short
Simplify the expression (3²)³ using the power of a power exponent rule.
Evaluate the principal square root: √81.
Evaluate the cube root: ∛64.
Which of the following numbers is an irrational number?
Find x
Write the standard number 45,000 in scientific notation.
Evaluate the negative exponent expression 5⁻².
Question · Medium
Simplify the quotient of powers: 4⁵ / 4².
Multiply the numbers in scientific notation: (3.0 × 10⁵) × (2.0 × 10³).
Two lines, one point: an emo ballad
Divide the numbers in scientific notation: (8.4 × 10⁷) ÷ (2.1 × 10³).
Add the numbers in scientific notation: (4.2 × 10⁴) + (3.5 × 10³).
Between which two consecutive integers does √50 lie?
Solve the quadratic equation x² = 144 for all real solutions.
Solve the cubic equation y³ = 125.
Simplify the expression (2³ × 2⁻⁵)² to fractional form.
Convert 0.00038 into scientific notation.
Subtract the numbers in scientific notation: (9.1 × 10⁶) - (6.5 × 10⁵).
Question · Hard
Order the following real numbers from least to greatest: π, √8, 3.1, 3²/3.
Simplify the algebraic expression (a⁴ × b⁻³) / (a⁻² × b²) using positive exponents.
A red blood cell has a diameter of 8 × 10⁻⁶ meters. A grain of sand has a diameter of 2 × 10⁻³ meters. How many times larger is the diameter of the sand grain than the red blood cell?
Which set of ordered pairs represents a function?
Functions And Linear Relationships
Find the slope m of the line passing through points (0, 3) and (4, 11).
What is the y-intercept b of the linear function y = 4x - 7?
A rental car company charges a flat fee of $25 plus $0.15 per mile driven. Which equation models total cost C for m miles?
Does the table with points (1, 5), (2, 10), (3, 15), (4, 20) represent a linear function?
Which equation represents a non-linear function?
Find the value of f(x) = -3x + 8 when x = 4.
What is the slope of any horizontal line on a coordinate plane?
Compare rates of change: Function A is y = 5x + 2. Function B has table points (0, 1), (2, 9), (4, 17). Which function has a greater rate of change?
Find the equation of the line passing through (-2, 5) and (3, -5) in slope-intercept form.
A water tank fills at a constant rate. At t = 2 minutes, volume is 14 gallons; at t = 6 minutes, volume is 34 gallons. What was initial volume at t = 0?
A line has a y-intercept of 6 and an x-intercept of 3. What is its equation?
Which description characterizes a non-proportional linear relationship?
Function A: y = 3x - 4. Function B passes through (1, 2), (3, 8), (5, 14). Which function has a greater initial value (y-intercept)?
Is the set of ordered pairs {(2, 3), (4, 5), (6, 7), (2, 9)} a function?
A runner maintains a constant speed of 6 miles per hour. Distance d = 6t miles for t hours. What is the practical domain for a 2-hour race?
A line has slope m = -3/4 and passes through (4, 2). Find its y-intercept b.
Height of a candle in inches after h hours is modeled by y = -0.8h + 10. What does -0.8 represent?
For the linear function with table values (-1, 7), (0, 4), (1, 1), (2, -2), find slope m.
How are the graphs of y = 2x and y = 2x + 4 related geometric lines?
Plan A costs $30 flat plus $0.05 per text. Plan B costs $15 flat plus $0.10 per text. At how many texts x do both plans cost the exact same amount?
Function 1 is f(x) = (x - 2)² + 1. Function 2 is g(x) = 2x + 1. Which statement correctly compares their linearity?
A line passing through points (k, 8) and (4, 2) has a slope of 3. Find the value of k.
Find the average rate of change of y = 2x² between x = 1 and x = 3.
A pool is draining at a constant rate. At 1 PM (t = 1 hour), volume is 800 gallons. At 4 PM (t = 4 hours), volume is 350 gallons. Write linear model V(t) for remaining volume.
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