Exponent Rules
Exponents and Powers · Class VIII
Verify a^m * a^n = a^(m+n) and (a^m)/(a^n) = a^(m-n) by sliders.
- a^m * a^n32
- a^{m+n}32
- (a^m) / (a^n)2
- a^{m-n}2
- y = a^x
Formulas in this lab
- a^m * a^n
- a^{m+n}
- (a^m) / (a^n)
- a^{m-n}
Frequently asked questions
▶What are the main exponent rules?
Two key rules: $a^m \cdot a^n = a^{m+n}$ and $a^m / a^n = a^{m-n}$. So 2^3 * 2^2 = 2^5 = 32 and 2^5 / 2^2 = 2^3 = 8. The lab verifies both rules numerically for any base and exponents you slide.
▶How do I use the exponent rules lab?
Slide base a (1 to 5), and exponents m and n (-5 to 5). The lab shows a^m * a^n side by side with a^(m+n) so you can confirm they always match. Try a = 3, m = 2, n = 4 to see both give 729.
▶What does a negative exponent mean?
A negative exponent means reciprocal: $a^{-n} = 1/a^n$. So 2^-3 = 1/8 = 0.125. The lab lets you set m or n to negative values and watch the answer shrink, which helps prepare you for higher-class topics.
▶Same base vs different base: do exponent rules still work?
The rules $a^m \cdot a^n = a^{m+n}$ require the same base a. They do not apply to 2^3 * 3^2; you must just compute that directly as 8 * 9 = 72. The lab keeps a single base so you always see the rule working safely.