Which is equivalent to 4⁻²? — 1/16.4⁻² = 1/4² = 1/16.
Which rule justifies: (aᵐ)ⁿ = aᵐⁿ? — Power of a power rule.(aᵐ)ⁿ = aᵐⁿ is the power-of-a-power rule (multiply exponents when a power is raised to another power).
What does a negative exponent tell you to do? — Take the reciprocal of the base raised to the positive exponent.a⁻ⁿ = 1/aⁿ. The negative exponent means "move to the denominator and make the exponent positive."
Write 4,500,000 in scientific notation. — 4.5 × 10⁶.Move the decimal 6 places to the left: 4.5 × 10⁶. The coefficient must be between 1 and 10.
Write 0.0000072 in scientific notation. — 7.2 × 10⁻⁶.Move decimal 6 places right to get 7.2; since it is a small number, exponent is negative: 7.2 × 10⁻⁶.
Convert 3.08 × 10⁴ to standard form. — 30,800.Move decimal 4 places right: 3.08 → 30,800.
Convert 6.1 × 10⁻³ to standard form. — 0.0061.Negative exponent → move decimal left: 6.1 → 0.0061.
Which number is written correctly in scientific notation? — 5.3 × 10⁴.Only 5.3 × 10⁴ has a coefficient between 1 and 10. The others violate the definition.
Which exponent makes this true: 0.0045 = 4.5 × 10? — 10⁻³.Moving the decimal 3 places right gives 4.5 from 0.0045, so the exponent is −3.
Which real-world quantity is best measured in scientific notation? — The number of atoms in a grain of sand (~10²⁰).Scientific notation is most useful for extremely large or small quantities. A grain of sand contains roughly 10²⁰ atoms — far too large for standard notation.
What is the slope of the line y = 4x − 3? — 4.In slope-intercept form y = mx + b, the slope is the coefficient of x. Here m = 4.
What is the y-intercept of y = −2x + 7? — 7.In y = mx + b, b is the y-intercept. Here b = 7.
Find the slope through (0, 3) and (2, 7). — 2.m = (7 − 3)/(2 − 0) = 4/2 = 2.
A line has slope 0. What does its graph look like? — A horizontal line.Slope 0 means no rise for any run — a perfectly horizontal line.
What is the slope of a vertical line? — Undefined.A vertical line has the same x for all y, so the run is 0. Division by zero is undefined.
Write the equation of a line with slope 3 and y-intercept −1. — y = 3x − 1.Substitute m = 3 and b = −1 into y = mx + b: y = 3x − 1.
Which method is most efficient when one equation is already solved for a variable? — Substitution.Substitution is most efficient when one equation is in the form y = … or x = … because you can directly substitute.
In a system, the graphs of two lines intersect at (−2, 5). What is the solution? — x = −2, y = 5.The solution of a system is the intersection point: (−2, 5), meaning x = −2 and y = 5.