Mathematics · Grades 6–8
Powers & roots · Formula sheet
Rules, conditions and small examples in one printable reference.
Remember this
Evaluate powers
The exponent counts factors, not additions.
aⁿ = a × a × … × a (n factors)
9 × 9 × 9 × 9 × 9 = 59049
Principal square roots
The principal square root is non-negative.
√(a²) = |a|
50 × 50 = 2500
Cube roots
Negative numbers have negative real cube roots.
∛(a³) = a
(5)³ = 125
Multiply powers of one base
Add exponents only when multiplying the same base.
aᵐ × aⁿ = aᵐ⁺ⁿ
10 + 3 = 13
Divide powers of one base
Subtract exponents; the base must not be zero.
aᵐ/aⁿ = aᵐ⁻ⁿ, a ≠ 0
5 − 5 = 0
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.