POWERS AND ROOTS
- Multiplying and Dividing Powers
To multiply powers with the same base, add the exponents and keep the same base:
x^3 × x^4 = x3+4 = x^7To divide powers with the same base, subtract the exponents and keep the same base:
y^13 ÷ y^8 = y13−8 = y^5- Raising Powers to Powers
To raise a term that already has exponents to another power, multiply the exponents:
(x^3 )^4 = x3×4 = x^12
Simplifying Square Roots
To simplify a square root, factor out the perfect squares under the radical, unsquare them, and put the result in front:
Adding and Subtracting Roots
You can add or subtract radical expressions when the part under the radicals is the same:
Don’t try to add or subtract when the radical parts are different. There’s not much you can do with an expression like this one:
- Multiplying and Dividing Roots
The product of square roots is equal to the square root of the product:
The quotient of square roots is equal to the square root of the quotient: