Problem
1 Express each of the following in index form. a $3 \times 3 \times 3 \times 3$ b $2 \times x \times x \times x \times y \times y$ c $3 \times a \times a \times a \times \frac{b}{a} \times b$ d $\frac{3}{5} \times \frac{3}{5} \times \frac{3}{5} \times \frac{1}{7} \times \frac{1}{7}$ 2. Write the following as a product of prime factors in index form. a 45 b -300
Solution
Step 1 ：The question is asking to express the given expressions in index form. Index form is a way of writing numbers using exponents. For example, \(2 \times 2 \times 2\) can be written in index form as \(2^3\).
Step 2 ：For the first question, we have \(3 \times 3 \times 3 \times 3\). This can be written in index form as \(3^4\).
Step 3 ：Here, the base is 3 and the exponent is 4, so the index form is \(3^4\).
Step 4 ：Final Answer: The expression \(3 \times 3 \times 3 \times 3\) in index form is \(\boxed{3^4}\).
