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(ax^n)^{1/3} = 7x^2 Work out the value of a and the value of n. - Edexcel - GCSE Maths - Question 13 - 2021 - Paper 3

Question 13

$(ax^n)^{1/3}-=-7x^2--Work-out-the-value-of-a-and-the-value-of-n.-Edexcel-GCSE Maths-Question 13-2021-Paper 3.png$

(ax^n)^{1/3} = 7x^2 Work out the value of a and the value of n.

Worked Solution & Example Answer:(ax^n)^{1/3} = 7x^2 Work out the value of a and the value of n. - Edexcel - GCSE Maths - Question 13 - 2021 - Paper 3

Step 1

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Answer

To find the value of a, we need to rewrite the equation. First, we raise both sides to the power of 3:

$(ax^n) = (7x^2)^3$

Calculating the right side gives:

$7^3 x^{2*3} = 343x^6$

This means we must have:

$ax^n = 343x^6$

From this equality, we can deduce that:

a = 343\ Thus, the value of a is 343.

Step 2

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Answer

Continuing from our previous equation:

$ax^n = 343x^6$

Since the bases of x are the same, we can compare the exponents. Therefore:

We find that the value of n is 6.

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