70 n 5 70 n 6 2 For what value of x is the given expression equivalent to 70 n

Question

70 n 5 70 n 6 2 For what value of x is the given expression equivalent to 70 n 30 x , where n &#62; 1 ?

Accepted Answer

The correct answer is 4 225 . An expression of the form a k , where k is an integer greater than 1 and a &#8805; 0 , is equivalent to a 1 k . Therefore, the given expression, where n &#62; 1 , is equivalent to 70 n 1 5 70 n 1 6 2 . Applying properties of exponents, this expression can be rewritten as 70 n 1 5 70 n 1 6 &#183; 2 , or 70 n 1 5 70 n 1 3 , which can be rewritten as 70 n 1 5 + 1 3 , or 70 n 8 15 . It's given that the expression 70 n 5 70 n 6 2 is equivalent to 70 n 30 x , where n &#62; 1 . It follows that 70 n 8 15 is equivalent to 70 n 30 x . Therefore, 8 15 = 30 x . Dividing both sides of this equation by 30 yields 8 450 = x , or 4 225 = x . Thus, the value of x for which the given expression is equivalent to 70 n 30 x , where n &#62; 1 , is 4 225 . Note that 4/225, .0177, .0178, 0.017, and 0.018 are examples of ways to enter a correct answer.

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