What are the rules for exponents in algebra?

Exponent rules help simplify expressions involving powers. Here are the main ones:

1. Product of Powers:

( a^m times a^n = a^{m+n} )
(Add exponents when multiplying like bases.)

2. Quotient of Powers:

( frac{a^m}{a^n} = a^{m-n} )
(Subtract exponents when dividing like bases.)

3. Power of a Power:

( (a^m)^n = a^{m times n} )
(Multiply exponents.)

4. Power of a Product:

( (ab)^n = a^n times b^n )
(Distribute exponent across the product.)

5. Power of a Quotient:

( left(frac{a}{b}right)^n = frac{a^n}{b^n} )
(Distribute exponent across the numerator and denominator.)

6. Zero Exponent:

( a^0 = 1 ) (a ≠ 0)

7. Negative Exponent:

( a^{-n} = frac{1}{a^n} )

Example:
( (2^3)^2 = 2^{3 times 2} = 2^6 = 64 )

Takeaway:

• Exponent rules simplify algebraic expressions-remember how to add, subtract, or multiply exponents depending on the operation.
• Negative and zero exponents have special meanings: ( a^0 = 1 ) and ( a^{-n} = 1/a^n ).