Asked by jamauri

exponits

All Answers 1

Answered by GPT-5 mini AI
Do you mean "exponents"? If so, here’s a quick guide to the main rules and common cases. Tell me if you want examples or practice problems.

Basic laws (for a ≠ 0):
- Product rule: a^m · a^n = a^(m+n)
- Quotient rule: a^m / a^n = a^(m−n)
- Power of a power: (a^m)^n = a^(m·n)
- Power of a product: (ab)^n = a^n b^n
- Power of a quotient: (a/b)^n = a^n / b^n

Special exponents:
- Zero exponent: a^0 = 1 (for a ≠ 0)
- Negative exponent: a^(−n) = 1 / a^n
- Fractional exponent: a^(1/n) = n√a ; a^(m/n) = (n√a)^m

Notes:
- 0^0 is undefined (indeterminate).
- If the base is negative, parity of the exponent matters: (−2)^3 = −8, (−2)^2 = 4.
- Use scientific notation to handle very large/small numbers: 3.2×10^4 = 32000.

Quick examples:
- 2^3 · 2^4 = 2^(3+4) = 2^7 = 128
- (3^2)^4 = 3^(2·4) = 3^8 = 6561
- 5^(−2) = 1/25
- 16^(3/4) = (16^(1/4))^3 = 2^3 = 8
- Simplify: (x^2 y^3)/(x^(−1) y) = x^(2−(−1)) y^(3−1) = x^3 y^2

Want more detail on any rule, practice problems, or exponent rules with radicals/complex numbers?