Vocabulary
For which property do you keep the base and subtract the exponents?
Quotient Rule
2^-1 = 1/2
Negative Exponent
Simplify.
5^2 * 5^10
5^12
Simplify.
2^15/2^8
2^7
Simplify
(12^8 a ^2)^3
12^24 a ^ 6
Which property tells you to keep the base and multiply the exponents.
Power to a Power Rule
x^5/x^3 = x ^(5-3)
Quotient Rule
Simplify.
(9 * 12)^5
9^5 * 12^5
Simplify.
(2/(ab))^12
2^12/(a^12 b ^12)
Simplify
(b^12)^7 / (a ^2)
b^84 / a ^2
For which property do you take the reciprocal of the negative power?
Negative exponents
(5 * 3)^0 = 1
Zero Rule
Simplify.
a^7 * a^14
a^21
Simplify
(a^7b)/a^5
a^2b
Simplify
(x/b)^0
1
Which property tells you to raise each factor to the exponent on the outside of the parentheses?
Product to a Power Rule
(4^2)^3 = 4^6
Power to a Power Rule
Simplify
(4m^6n^2)^3
4^3 m ^18 n ^ 6
Simplify
(3 x ^3 y^ 7 z ^ 9)/ (2 x^ 2 z ^5)
(3 x y ^7 z ^ 4)/2
Simplify
(r^2)/(4r^4)
1/ (4r^2)
Any number/variable to the power of zero is equal to 1
Zero Power
1/(3)^-5 = 3 ^5
Negative exponent
Simplify
(x * y^2)^5 * x^3
x^8 * y^10
Simplify
(x^10y^8z^2)/(x^3y^4z)
x^7y^4z
Simplify
(a^2 * b^3)^2
a^4 *b^6