Mathematics · Grades 8–12
Exponent rules with the missing conditions
Read the domain restrictions, especially around zero and fractional powers.
Understand the idea
Product
For integer powers, use values where each expression is defined.
a^m × a^n = a^(m+n)
2³ × 2⁴ = 2⁷.
Quotient
Division by zero is not permitted.
a^m / a^n = a^(m−n), a ≠ 0
5⁶ / 5² = 5⁴.
Power of a power
Safe here for integer exponents with defined expressions; fractional powers need care.
(a^m)^n = a^(mn)
(3²)⁴ = 3⁸.
Zero exponent
Do not infer a universal value for 0⁰ from this rule.
a⁰ = 1 for a ≠ 0
7⁰ = 1.
Negative exponent
A negative exponent means reciprocal, not a negative value.
a^(−n) = 1/a^n, a ≠ 0
2^(−3) = 1/8.
Square root
The principal square root is nonnegative.
√(x²) = absolute value of x for real x
√((-5)²) = 5.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Preview material · independent educational review required. Grade bands are approximate, not official curriculum alignment.