Product Rule
Power Rule
Quotient Rule
Negative Exponent Rule
Rational Exponents & Radical Form
Simplifying Radicals
100
When multiplying variables, you do this to the exponents.
What is adding?
100
When a power is raised to a power, you do this to the exponents.
What is multiplying?
100
When dividing variables, you do this to the exponents.
What is subtracting?
100
When dealing with negative exponents, you do this to the exponents.
What is flip them to the denominator? (Or flip them to the opposite part of the fraction.)
100
Convert the radical expression to a rational exponent.
x^(2/3)
100
You use this list as the first step to simplify radicals.
What is perfect squares?
200
2x^5 * x^7
2x^12
200
4(y^3)^2
4y^6
200
(2x^6)/(6x^5)
(1x)/3 OR
(1/3)x
200
x^-3 / x^3
1/x^6
200
Convert the radical expression to a rational exponent.
7^(3/4)
200
Simplify:
sqrt(12)
2sqrt3
300
(4f^8)(6f^4)
24f^12
300
(x^3y^2)^6
x^18y^12
300
(8x^10)/(4x^3)
2x^7
300
(3x^-8)(6x^4)
18/(x^4)
300
Convert the rational exponent to a radical expression.
+^9sqrt(b^7
300
Simplify:
sqrt(50)
5sqrt2
400
(8r^5)(2r^7)
16r^12
400
(4w^5)^2
16w^10
400
(w^6u^9)/(w^3u^2)
w^3u^7
400
(x^-3v^5)^-8
x^24/(v^40)
400
Convert the radical expression to a rational exponent.
b^(5/11)
400
Simplify.
2sqrt3 + sqrt27
5sqrt3
500
(7s^5p^3)(3s^6p^5)
(21s^11p^8)
500
(8w^3y^7)^0
1
500
(4x^8m^8x^5)/(8x^2m^4)
(1/2) x^6m^4x^5 OR
(1x^6m^4x^5)/2
500
11a^2 * 3a^-6
33/a^4
500
Convert the radical expression to a rational exponent.
(y^4z^2)^(1/6) OR
y^(4/6)z^(2/6)
500
Simplify:
2sqrt3 * 4sqrt15
24sqrt5