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1. Can you simplify the product of the radical expressions? Explain.
   1. 7 4 ⋅ 7 5 the fourth , root of 7 , , dot , the fifth , root of 7 ,
   2. − 5 5 ⋅ − 2 5 the fifth , root of negative 5 end root , , dot , the fifth , root of negative 2 end root ,

Problem 2 Simplifying a Radical Expression

What is the simplest form of 54 x 5 3 ? cube root of 54 , x to the fifth end root , . question mark

54 x 5 3 = 3 3 ⋅ 2 ⋅ x 2 ⋅ x 3 3 Find all perfect cube factors .   = 3 3 x 3 3 ⋅ 2 x 2 3 a b n = a n ⋅ b n   = 3 x 2 x 2 3 Simplify . table with 3 rows and 3 columns , row1 column 1 , cube root of 54 , x to the fifth end root , , column 2 equals . cube root of 3 cubed , dot 2 dot , x squared , dot , x cubed end root , , column 3 cap findallperfectcubefactors . . , row2 column 1 , , column 2 equals . cube root of 3 cubed , x cubed end root , . dot . cube root of 2 , x squared end root , , column 3 the th , root of eh b end root , , equals , the th , root of eh , , dot , the th , root of b , , row3 column 1 , , column 2 equals 3 x . cube root of 2 , x squared end root , , column 3 cap simplify , . , end table

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2. What is the simplest form of 128 x 7 3 ? cube root of 128 , x to the seventh end root , . question mark

Problem 3 Simplifying a Product

What is the simplest form of 72 x 3 y 2 ⋅ 10 x y 3 ? square root of 72 , x cubed , y squared end root . dot . square root of 10 x , y cubed end root . question mark

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3. What is the simplest form of 45 x 5 y 3 ⋅ 35 x y 4 ? square root of 45 , x to the fifth , y cubed end root . dot . square root of 35 x , y to the fourth end root . question mark