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

(ii) Find p if 3^p = 3 square root 9/3-example-1
User Jeremy Allen
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1 Answer

16 votes
16 votes

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)

User Smchae
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