1. Radicals without Calculators
Section 6-5 : Powers and
Radicals without Calculators
It is important to be able to evaluate expressions without the use of a calculator. In order to do this you will need to break the expression up into smaller simpler parts.
Example:
Change from exponents to roots
Simplify by changing to cube root that are common to use
Simplify those common roots

2. We might want to split an expression up before we change to the roots
We might want to split an expression up before we change to the roots. Example:
Split the exponent up by using the properties of exponents
Now you only need to change one number to a simple cube root
Evaluating that root and then multiplying you obtain your answer

3. In some cases you might need to address a negative exponent Example:
Change the exponent from being negative to positive, then split the exponent up by using the properties of exponents
Now you only need to change one number to a simple 5th root
Evaluating that root and then multiplying you obtain your answer

4. Another example of a negative exponent. Example:
The negative exponent switches your numerator and denominator
Now take the square root of the fraction and cube that answer

5. In the following examples we need to change the numbers so we have a common base, then we can set the exponents equal to each other and solve to find the value of the variable. Example:
Change both numbers to an exponent with a base of 2
Properties of exponents to multiply 2 times x
With the same base for the statement to be true the exponents must be equal, set up an equation with them and solve

6. Another example: Change both numbers to an exponent with a base of 3
Properties of exponents to multiply 3 times x
With the same base for the statement to be true the exponents must be equal, set up an equation with them and solve

7. Page 251-252 Questions 16-36 evens, 53-59