13 (a) Work out 2^4 - OCR - GCSE Maths - Question 13 - 2018 - Paper 1

Given the equation:

$100 = 4 imes 5^n$

First, we can express 4 as $2^2$:

$100 = 2^2 imes 5^n$

We also express 100 in terms of its prime factors:

$100 = 10^2 = (2 imes 5)^2 = 2^2 imes 5^2$

Now we can equate the two sides:

$2^2 imes 5^n = 2^2 imes 5^2$

By comparing the coefficients of $5$, we find:

$n = 2$

Thus, the value of n is 2.