Answer: a = -2/3
Step-by-step explanation:
Let's start by multiplying both sides by [tex]x[/tex] to simplify:
[tex]$4^{1/3} = x^a \times x$[/tex]
[tex]$4^{1/3} = \underbrace{x \times x \times x \times \cdots \times x}_{a\ \textrm{times}} \times \,x$[/tex]
[tex]$4^{1/3} = \underbrace{x \times x \times x \times \cdots \times x \times x}_{a+1\ \textrm{times}}$[/tex]
[tex]4^{1/3} = x^{a+1}[/tex]
Looking only at the exponents, it seems like [tex]1/3 = a+1[/tex], so [tex]a = \boxed{-2/3}[/tex].
