I chose this topic because while it covers new forms of radicals such as mixed and entire, it also reviews previous topics such as exponent laws.
To be able to solve the following examples, you need pre-existing knowledge on order of operations, exponent laws, and fractions.
- Zero exponents:
= 1 - Negative exponents:
= 
(reciprocal) - Product of exponents:
- Quotient of exponents:
- Power of a power:
- Order of operations: Brackets, exponents, division/multiplication, addition/subtraction.
First, simplify out of the brackets. Looking at the exponents, use the power of a power rule to multiply. 3/2 * 2/1 = a^6/2 = a^3/1
Now look to completely simplify the first variable. Using the quotient of exponents rule, subtract. a^3 – a^3 = a^0 = 1
Simplify the second variable. b^3/1 = b^6/2, b^1/2 – b^6/2 = b^-5/2
Use negative exponents rule to simplify negative exponent to a positive. b^-5/2 = 1/b^5/2
Finally, recognize that fractional exponents show the radicand, index, and power for an entire radical. In this case, b^5/2 = 
So, the answer is:
