Product Rule
x^2*x^3
x^5
x^5/x^2
x^3
(a^2)^3
a^6
x^-1
1/x
(3x)^2
9x^2
(x/y)^2
(x^2/y^2)
When you multiply two of the same bases, you must add the exponents together.
Product Rule
2x^7*7x^9
14x^16
(2x^3)/(4x)
x^2/2
(ab^3)^5
a^5b^15
x^2/x^-5
x^7
(-3xy^3)^4
81x^4y^12
((2b^3f)/g)^3
(8b^9f^3)/(g^3)
When you divide two of the same bases, you must subtract the exponents together.
Quotient Rule
2ab*3a^2b^5
6a^3b^6
(x^3y)/(xy^2)
x^2/y
(2a^2b^6)^7
128a^14b^42
x^-2y^-1
1/(x^2y)
(3xy)^5
243x^5y^5
((4ab)/(8ab^2))^2
(1/(4b^2))
Anything raised to the zero power (except 0) will give you a result of 1.
2a^2b^3c^6*7a^2b^4c^2
14a^4b^7c^8
(9a^2b^3)/(64a^5b^7)
9/(64a^3b^4)
(2a^3b^4)^4
16a^12b^16
2x^-2y^3*-4x^4y^-5
(-8x^2)/y^2
(7x^3y^5)^2
49x^6y^10
((15bc)/(3b^2c^3))^2
25/(b^2c^4)
If the exponent is negative in the numerator or denominator, then you must switch it and change the exponent into a positive number.
Negative Exponent Rule
-3b^3f^4z^3*2bf^2
-6b^4f^6z^3
(15a^3b^4c^3)/(12a^3b^3c^10)
(5b)/(4c^7)
(7ab^2c^4)^2
49a^2b^4c^8
(2x^-3y^-4z^-6)/(4x^-2y^-1z^-5)
1/(2xy^3z)
(3a^2x^3 )^2 (2ax^4)^3
72a^7x^18
((75a^2b^3c^4)/(3abc))^2
625a^2b^4c^6
When a product is raised to a power, the result is the product of each factor raised to the power.
Power of a Product Rule