Laws of exponents

Check conditions and apply exponent laws.

Meaning

Add exponents when multiplying powers with the same base. Extending exponents to zero, negative numbers, and fractions also requires checking base and operation conditions.

Example

does not mean multiplying 2 a negative number of times; it is The first factor contains three copies of 2 and the second two, giving five altogether. For a nonzero base, decreasing the exponent by one divides by the base; continuing gives 2⁰=1 and 2⁻¹=Do not add exponents for different bases. The rule requires a nonzero base a.

Practice for this concept

Scope and references

Topics

Products and quotients of powers, powers of powers, extending exponents

Learning goal

Check conditions and apply exponent laws.

Helpful background

Explore repeated multiplication and what an exponent counts.

Exponent laws

These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.

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