sat-dog

m The correct answer is 361 . The rational exponent property is n y m= yn, where 8 > > y 0, m and n are integers, and n 0. This property can be applied to rewrite ( )( )( )( ) ( ) the given expression 6 5 3 5 x 45  8 2 8 x as 6 3 5 5 x 4 5 5 28 8 x8 1 , or 6 ( 3 )( x 9 )( 2 ) x8 1 . This expression can be rewritten by multiplying the constants, which gives ( ) 36 ( x 9 ) x8 1 . The multiplication exponent property is y n  y m= y n + m , where y > 0. ( ) ( ) 1 9 +1 This property can be applied to rewrite the expression 36 x 9 x8 as 36x 8, or 73 73 36x8. Therefore, 6 5 3 5 x 45  8 2 8 x = 36x8. It’s given that 6 5 3 5 x 45  8 2 8 x is b = =73 + = +73 equivalent to ax ; therefore, a 36 and b . It follows that a b 36 . 8 8 Finding a common denominator on the right-hand side of this equation gives + =288+73 + =361 a b , or a b . Note that 361/8, 45.12, and 45.13 are examples of 8 8 8 ways to enter a correct answer.