Tommy and Sally are arguing over the meanings of x^4 and x^-4. Tommy argues that x^4 is the reciprocal of x^-4. Sally insists that x^-4 is the reciprocal of x^4. Who is correct? A. Tommy is correct. x^4 is the reciprocal of x^-4. B. Sally is correct. x^-4 is the reciprocal of x^4. C. Both Tommy and Sally are correct. x^-4 and x^4 are the reciprocals of each other. D. Niether Sally nor Sally is correct. Neither x^-4 nor x^4 is a reciprocal of the other.

Question

Mathematics

Braden

12 June, 00:31

Tommy and Sally are arguing over the meanings of x^4 and x^-4. Tommy argues that x^4 is the reciprocal of x^-4. Sally insists that x^-4 is the reciprocal of x^4. Who is correct? A. Tommy is correct. x^4 is the reciprocal of x^-4. B. Sally is correct. x^-4 is the reciprocal of x^4. C. Both Tommy and Sally are correct. x^-4 and x^4 are the reciprocals of each other. D. Niether Sally nor Sally is correct. Neither x^-4 nor x^4 is a reciprocal of the other.

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The answer is C because X^-4 is also expressed as 1/X^4. A reciprocal of a number is 1 divided by that number. Therefore, it is seen that X^-4 is the reciprocal of X^4. Also, the reciprocal of X^-4 is 1/X^-4 which becomes 1 / (1/X^4) simplifying to X^4. So X^4 is the reciprocal of X^-4, meaning both Sally and Tom are correct.