Use the properties of exponents to determine the value of aa for the equation: \frac{\sqrt[3]{4} }{x} =x^(a)

Question

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


`\frac{\sqrt[3]{4} }{x} =x^(a)`

Answer 1

Answer: a = -2/3

Explanation:

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

`$4^(1/3) = x^a * x$`

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

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

`4^(1/3) = x^(a+1)`

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