Expressions

Question

If the expression (2y^a)^4 is equivalent to 16y^2, what is the value of a

Answer 1

The equation

(2y^a)^4   =   16y^2

(2^4)(y^a)^4   =   16y^2             [ Since (ab)^m = a^m X b^m]

16(y^4a)   =   16y^2                   [ Since (a^m)^n = a^(mn)]

y^4a   =   y^2

As the bases are the same equate the exponents

4a   =   2

a   =   2/4

a   =   1/2

Hence, a = 1/2.