Can I multiply a norm to a quaternion?

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Let's say we have 2 quaternions a = 1+3i+5j+7k, b = 3+8i+12j+16k, can I multiply its norm to another quaternion? For example: ||a||(b)

Norm of a = $\sqrt{1^2+3^2+5^2+7^2}$ = 9.16515...

Should I do it like simple maths? 9.16515(3+8i+12j+16k) = 27.49 + 73.32i + 109.98j + 146.64

Or should I turn the norm into a quaternion first(9.16515+9.16515i+9.16515j+9.16515k), then calculate the Hamilton product of them? Multiplication Method

Thank you for your help!!