The answer to the first equation needs to have a numerator and denominator because the exponent is negative. When you raise a number to a negative exponent, the result is the reciprocal of the number raised to the positive version of the exponent. In this case, the exponent is -2, so the answer is 1/(y^14).
The answer to the second equation does not need to have a numerator and denominator because the exponent is positive. When you raise a number to a positive exponent, the result is the number raised to the exponent. In this case, the exponent is 5, so the answer is x^15.
With an equation like: (y^7)^-2,
why is the answer = 1/(y^14)
and then I look at a similar type of problem: (x^-3)^-5 = x^15.
How come one answer needs to have a numerator and denominator while the other is just simple like x^15?
2 answers
(x^a)^b = x^(ab)
you just multiply the exponents; the usual rules for signs are used.
you just multiply the exponents; the usual rules for signs are used.