(ax^n)^{1/3} = 7x^2 Work out the value of a and the value of n. - Edexcel - GCSE Maths - Question 15 - 2021 - Paper 3

To find the values of a and n, start by rewriting the equation:

$(ax^n)^{1/3} = 7x^2$.

Next, apply the power of a power property, which states that $(x^m)^n = x^{mn}$. Thus, we can rewrite the left-hand side as:

$(a^{1/3})(x^{n/3}) = 7x^2$.

From this equation, we can equate the coefficients and powers of x.

Since the right side has $x^2$, we have:

$\frac{n}{3} = 2 \Rightarrow n = 6.$

Now, to find the value of a, we equate the constants on both sides:

$a^{1/3} = 7 \Rightarrow a = 7^3 = 343.$