Analytic Geometry Unit 4 Worksheet #5 Name____________________________ Simplify the expressions using the properties of radicals and rational exponents Ex) ( ) Ex) ( ( ) ) ( Ex) Ex) √ Ex) √ √ ) √ √ √ √ Ex) [( ) ] Ex) √( ) ( ) Ex) ( ) [( ) ] ( ) (√ ) √ √ √ √ √ Simplify the expressions. Assume all variables are positive Ex) √ Ex) ( ) To solve equations such as , we take the cube root of both sides. Alternately, we can raise both sides of the equation to the power. That is, we raise both sides of the equations to the power that is the inverse ( or reciprocal) of the power in the problem. To solve , we can either square both sides and then take the cube root, we can take the cube root of both sides and then square them, or we can raise both sides to the power. ( ) ( ) Rewrite each of the following using rational exponents and use inverses to solve for the variable. (You may need to use a calculator for some of them. Be careful!) Ex) √ Ex) √ ( ) Ex) √ ( ) ( ( ) ) Complete this assignment on notebook paper Simplify the expression using the properties of radicals and rational exponents 2) √ 1) 5) 4) ( ) 7) ( ) √ 3) √ √ 6) ( ) √ √ 8) √ √ 9) √( ) ( ) Simplify the expression. Assume all variables are positive 12) √ 11) √ 10) √ 14) 13) 17) √( 16) √ √ 15) ( ) ( ) 18) ) √ √ Perform the indicated operation. Assume all variables are positive 19) √ √ ( 20) ) ( ) 21) √ √ Rewrite each of the following using rational exponents and use inverses to solve for the variable 22) √ 23) 24) √ √ Review 25) A metalworker wants to make an open box from a sheet of metal. It will be formed by cutting equal squares from each corner as shown. Write the standard form of the polynomial expression that represents the volume of the box. 12 in x x 16 in

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