8 (a) Write $3 \times 3 \times 3 \times 3$ as a power of 3 - OCR - GCSE Maths - Question 8 - 2020 - Paper 1

First, let's simplify the expression $2^{6} \times 4^{-1}$.

We can rewrite $4$ as $2^{2}$:

$4^{-1} = (2^{2})^{-1} = 2^{-2}.$

Replacing $4^{-1}$ in the original expression gives:

$2^{6} \times 4^{-1} = 2^{6} \times 2^{-2}.$

Now, we can combine the exponents by using the property of exponents $a^{m} \times a^{n} = a^{m+n}$:

$2^{6 - 2} = 2^{4}.$

Notice that $2^{4}$ can be expressed as:

$2^{4} = (2^{2})^{2}.$

Since it is in the form of $(a^{b})^{c}$, this confirms that $2^{4}$ is indeed a square number. Therefore, we have shown that $2^{6} \times 4^{-1}$ is a square number.