Question

Which of the following are equivalent to (y + 3)4/9?9A. (Wy+3)B. V(y + 3)*4c. (Ny+3)D. (x+3)(y9

Answer 1

ANSWER

B and C

EXPLANATION

The given expression has a fractional exponent. In a fractional exponent, the numerator is what we usually write as a power and the denominator is what we write as a root,

$a^{m/n}=\sqrt[n]{a^m}$

In this case, option B shows this same form,

$(y+3)^{4/9}=\sqrt[9]{(y+3)^4}$

The power and the root are exchangeable because we can separate them as "power of a power" which is the product of the exponents - and the order of the factors does not matter.

Hence, option C is also equivalent,

$(y+3)^{4/9}=\sqrt[9]{(y+3)^4}=(\sqrt[9]{(y+3)})^4$