The value of x^y is how many times the value of [(x^y)(x^(y+1))(x^(y+2))(x^(y+3))]/x?
A. x^y
B. x^(4y+5)
C. x^(4y+6)
D. x^(-3y-5)
E. x^(-4y-5)
A. x^y
B. x^(4y+5)
C. x^(4y+6)
D. x^(-3y-5)
E. x^(-4y-5)
When you're multiplying numbers with the same base and different exponents, you simply need to add all the exponents together. Similarly, dividing by a number with the same base means subtracting that exponent.
As such, the expression can be simplified to:
[(x^y)(x^(y+1))(x^(y+2))(x^(y+3))]/x = x^(y+y+1+y+2+y+3) / x^1 = x^(y+y+1+y+2+y+3-1) = x^(4y+5)
Notice that the question does not simply ask you to simplify the expression, but rather asking you to compare it in size to x^y
x^y / x^(4y+5) = x^(y-4y-5).
Simplify to get D as the answer.
