Express the following in index form: a) 81 b) 1/16

Here are the solutions to your mathematics questions.

1. Laws of Indices and Logarithms

• a) Express the following in index form:

  • i) 81

    Step 1: Find the prime factors of 81.

    $$81 = 3 \times 3 \times 3 \times 3$$

    Step 2: Write in index form.

    $$81 = 3^4$$

    The index form is $\boxed{3^4}$.

  • ii) $\frac{1}{16}$

    Step 1: Express 16 in index form.

    $$$$