The laws of exponents are rules that describe how to handle mathematical operations involving powers. Here are the key laws: 1. Product of Powers: a^(m) × aⁿ = a^(m+n) 2. Quotient of Powers: (a^(m))/(aⁿ) = a^(m−n) 3. Power of a Power: (a^(m))ⁿ = a^(m · n) 4. Power of a Product: (ab)ⁿ = aⁿ × bⁿ 5. Power of a Quotient: (a/b)ⁿ = (aⁿ)/(bⁿ) 6. Zero Exponent: a⁰ = 1 (a ≠ 0) 7. Negative Exponent: a⁻ⁿ = (1)/(aⁿ) (a ≠ 0) These laws help simplify expressions involving exponents. If you need examples or specific problems using these laws, let me know!

Laws of exponent

September 19, 2026Mathematics

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The laws of exponents are rules that describe how to handle mathematical operations involving powers. Here are the key laws:

Product of Powers
$a^{m} \times a^{n} = a^{m+n}$
Quotient of Powers
$\frac{a^{m}}{a^{n}} = a^{m-n}$
Power of a Power
$(a^{m})^{n} = a^{m \cdot n}$
Power of a Product
$(ab)^{n} = a^{n} \times b^{n}$
Power of a Quotient
$\left(\frac{a}{b}\right)^{n} = \frac{a^{n}}{b^{n}}$
Zero Exponent
$a^{0} = 1 \quad (a \neq 0)$
Negative Exponent
$a^{-n} = \frac{1}{a^{n}} \quad (a \neq 0)$
These laws help simplify expressions involving exponents. If you need examples or specific problems using these laws, let me know!

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Laws of exponent

Step-by-step solution

Product of Powers

Quotient of Powers

Power of a Power

Power of a Product

Power of a Quotient

Zero Exponent

Negative Exponent

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