Exponents

Practice 5 items →

Exponent laws are names for counting factors; negative exponents are reciprocals. Students simplify monomial quotients, convert between rational exponents and radicals, add and multiply simple radicals, and operate in scientific notation.

Specification · for a parent or teacher
Part no.
laws-of-exponents
Course
High School Math 1 · Unit 1
Realm
Numbers
Difficulty
3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

apply the seven laws to simplify monomial quotients with negative exponents; convert am/n↔amna^{m/n}\leftrightarrow\sqrt[n]{a^m} and evaluate; add, subtract, multiply simple radicals (8+18=52\sqrt{8}+\sqrt{18}=5\sqrt2); multiply and divide in scientific notation.

Ready when

12x−3y44x2y−1\frac{12x^{-3}y^4}{4x^2 y^{-1}} simplified, and 82/38^{2/3} evaluated as 4.

Formulas

Product and quotient
aman=am+n,aman=am−na^m a^n = a^{m+n},\quad \frac{a^m}{a^n} = a^{m-n}
Power of a power
(am)n=amn(a^m)^n = a^{mn}
Negative and rational
a−n=1an,am/n=amna^{-n} = \frac{1}{a^n},\quad a^{m/n} = \sqrt[n]{a^m}

Watch for

23⋅24=2122^3\cdot 2^4=2^{12}; 3−2=−93^{-2}=-9; a+b=a+b\sqrt{a+b}=\sqrt a+\sqrt b.

Before · requires

After · used by

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laws-of-exponents

Items: laws-of-exponents-01 · laws-of-exponents-02 · laws-of-exponents-03 · laws-of-exponents-04 · laws-of-exponents-05