Question

(ii) Find p if 3^p =
3 square root 9/3

Answer 1

Key Concepts

• Exponent Rules

We must know the following exponent rules to help us solve this question:

1. 
   `a^(m)/(n)=\sqrt[n]{a^m}`
2. 
   `(a^m)/(a^n)=a^(m-n)`
3. 
   `(a^m)^n=a^(mn)`
4. 
   `a^m=a^n, \therefore m=n`

Solving the Question

`3^p=\frac{\sqrt[3]{9}}{3}`

⇒ Rewrite
`\sqrt[3]{9}` as
`9^(1)/(3)`:

`3^p=((3^2)^(1)/(3))/(3)`

⇒ Multiply:

`3^p=(3^(2)/(3))/(3)`

⇒ Subtract:

`3^p=3^{(2)/(3)-1}`

`p=(2)/(3)-1\\\\p=-(1)/(3)`

Answer

`p=-(1)/(3)`