Zero exponent
NMT\[a^0=1\]
Condition
\(a\ne0\)
NMT / ZNO
Formulas and reference
A compact mathematics reference in two levels: the NMT exam sheet and the full ZNO formula set.
ZNO — full reference
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Algebra
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11 formulas
Full ZNO
Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Powers and roots
Powers
Negative integer exponent
NMT\[a^{-n}=\frac1{a^n}\]
Condition
\(a\ne0,\ n\in\mathbb N\)
Product of powers
NMT\[a^m a^n=a^{m+n}\]
Quotient of powers
NMT\[\frac{a^m}{a^n}=a^{m-n}\]
Condition
\(a\ne0\)
Power of a power
NMT\[(a^m)^n=a^{mn}\]
Power of a product
NMT\[(ab)^n=a^n b^n\]
Power of a quotient
NMT\[\left(\frac ab\right)^n=\frac{a^n}{b^n}\]
Condition
\(b\ne0\)
Rational exponent
NMT\[a^{\frac mn}=\sqrt[n]{a^m}\]
Condition
\(a\gt 0,\ m\in\mathbb Z,\ n\in\mathbb N,\ n\ge2\)
Powers and roots
Roots
Square root of a square
NMT\[\sqrt{a^2}=|a|\]
Root of a product
\[\sqrt{ab}=\sqrt a\sqrt b\]
Condition
\(a\ge0,\ b\ge0\)
Root of a quotient
\[\sqrt{\frac ab}=\frac{\sqrt a}{\sqrt b}\]
Condition
\(a\ge0,\ b\gt 0\)
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