The expression 6 3 5 x 45 5 · 2 8 x 8 is equivalent to a x b ,

Question

The expression 6 3 5 x 45 5 &#183; 2 8 x 8 is equivalent to a x b , where a and b are positive constants and x &#62; 1 . What is the value of a + b ?

Accepted Answer

The correct answer is 361 8 . The rational exponent property is y m n = y m n , where y &#62; 0 , m and n are integers, and n &#62; 0 . This property can be applied to rewrite the given expression 6 3 5 x 45 5 &#183; 2 8 x 8 as 6 3 5 5 x 45 5 2 8 8 x 1 8 , or 6 3 x 9 2 x 1 8 . This expression can be rewritten by multiplying the constants, which gives 36 x 9 x 1 8 . The multipliion exponent property is y n &#183; y m = y n + m , where y &#62; 0 . This property can be applied to rewrite the expression 36 x 9 x 1 8 as 36 x 9 + 1 8 , or 36 x 73 8 . Therefore, 6 3 5 x 45 5 &#183; 2 8 x 8 = 36 x 73 8 . It's given that 6 3 5 x 45 5 &#183; 2 8 x 8 is equivalent to a x b ; therefore, a = 36 and b = 73 8 . It follows that a + b = 36 + 73 8 . Finding a common denominator on the right-hand side of this equation gives a + b = 288 8 + 73 8 , or a + b = 361 8 . Note that 361/8, 45.12, and 45.13 are examples of ways to enter a correct answer.

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