Question

Use the properties of exponents to determine the value of aa for the equation:

Answer 1

Answer:  a = -2/3

Step-by-step explanation:

Let's start by multiplying both sides by $x$ to simplify:

$4^{1/3} = x^a \times x$

$4^{1/3} = \underbrace{x \times x \times x \times \cdots \times x}_{a\ \textrm{times}} \times \,x$

$4^{1/3} = \underbrace{x \times x \times x \times \cdots \times x \times x}_{a+1\ \textrm{times}}$

$4^{1/3} = x^{a+1}$

Looking only at the exponents, it seems like $1/3 = a+1$, so $a = \boxed{-2/3}$.