Exponents Are Instructions, Not Decorations

You'll learnto read exponent and radical rules correctly, and answer the exact quantity the item asks.

Exponents and radicals are compact instructions, not ornaments hung on a base. The points leak in four predictable places: spreading a power across a sum, misreading a negative or fractional exponent, reaching for the wrong combine rule, and reporting a value the item never asked for.

8 STEPS · 6 QUICK CHECKS · a power spreads over products, not sums · v3

powers · roots · rules

Before you start

What you're looking at

A card explaining what an exponent means, beside a panel listing the three combine rules — multiply adds, divide subtracts, power multiplies. The card closes on the line the whole topic ends with: report the exact quantity the item asks for.

The question

Which rule matches each operation, and what does a negative or fractional exponent actually tell you to do?

Watch for

Each rule appears one at a time; watch that a power spreads over products, never over a sum.

What the symbols mean

x with an exponent means x multiplied that many times; a negative exponent means a reciprocal, a fractional exponent means a root.

The parts

1 · the setup → 2 · the three rules → 3 · products, not sums → 4 · negative exponents → 5 · fractional exponents → 6 · transfer — then the trap and the recap

Step 1 / 8