Utilize integer exponents' properties to form corresponding numerical expressions, such as 32 × 3–5 = 3–3 = 1/33 = 1/27. Represent solutions to equations like x2 = p and x3 = p using square and cube root symbols. Evaluate cube and square roots of small perfect cubes and squares, understanding that √2 is irrational.

Express very large or small quantities through numbers displayed as a single digit times an integer power of 10. For example, estimate US population as 3 × 108 and world population as 7 × 109, determining the world population is over 20 times larger. Execute operations with numbers in scientific notation, including problems where decimal and scientific notation are used. Use scientific notation and suitably sized unit for measurements of very large or incredibly small quantities (e.g., use millimeters per year for seafloor spreading). Recognize scientific notation generated by technology.

Plot proportional relationships, understanding the unit rate as the graph's slope. Compare different proportional relationships represented in varying ways, such as a distance-time graph vs a distance-time equation. Use similar triangles to explain why the slope m is constant between any two distinct points on a non-vertical