Percent Change & Exponent Rules

Multiplying by 1.07 for +7% · fractional exponents & radicals

Fixes these misses: M1 Q17 (percent), M1 Q16 (fractional exponents).

Core concepts

Percent change as a multiplier

Increase by p% → multiply by (1 + p/100). A 7% increase → ×1.07.
Decrease by p% → multiply by (1 − p/100). A 7% decrease → ×0.93.
Successive changes multiply: +10% then +20% → ×1.10×1.20 = ×1.32 (not +30%).

Exponent rules

x^a·x^b = x^a+b · x^a/x^b = x^a−b · (x^a)^b = x^ab.
(xy)^a = x^ay^a.

Fractional exponents & radicals

x^(1/n) = ⁿ√x , x^(a/b) = ^b√(x^a)

Rewrite radicals as fractional exponents to combine them cleanly.
⁷√(x⁹y⁹) = (x⁹y⁹)^(1/7) = x^(9/7)y^(9/7).

Worked example — a clean percent multiplier

Problem. City A’s population rose 7% from 2015 to 2016. If 2016 = k × 2015, what is k?

A 7% increase means multiply by 1 + 0.07 = 1.07.

So k = 1.07 (this is the M1 Q17 answer).

Watch out: "+7%" is ×1.07, not ×0.07 and not ×1.7. This is a one-line idea but it cost a point on M1 Q17. For exponents, rewrite every radical as a fractional power before combining — don’t guess.

Video lessons

Curated walkthroughs from trusted math channels — watch one or two before doing the worksheet.

Khan Academy

Percent increase as a multiplier

Why +7% means ×1.07 — fixes M1 Q17

Organic Chemistry Tutor

Exponent rules explained

Product, quotient, power & negative exponents

Khan Academy

Fractional exponents & radicals

x^(a/b) = ^b√(x^a) — fixes M1 Q16

SAT/PSAT prep

Successive percent changes

Why +10% then +20% is not +30%

Ready to practice? Open the Percent Change & Exponent Rules worksheet →