1. Simplify: (a) $m' \times m^n$ (b) Simplify $ (5my)^2 $ (c) Simplify $ \frac{32q^2r^1}{4q^1r} $ - Edexcel - GCSE Maths - Question 3 - 2018 - Paper 2

To simplify the expression $(5my)^2$, we apply the power of a product property. This states that we can square each factor inside the parentheses. Therefore, we have:

$(5my)^2 = 5^2 \times m^2 \times y^2 = 25m^2y^2$

To simplify the expression $\frac{32q^2r^1}{4q^1r}$, we divide the coefficients and subtract the exponents of like bases. First, we simplify the coefficients:

$\frac{32}{4} = 8$

Next, we simplify the $q$ terms:

$q^{2-1} = q^1 = q$

And for the $r$ terms:

$\frac{r^1}{r^1} = 1$

Putting it all together, we get:

$\frac{32q^2r^1}{4q^1r} = 8q$