Question

find the value of c in the equation a^b(4a^b)^c=1024a^6b

Answer 1

This looks a bit bulky but use your index laws to gradually simplify the LHS of the equation.

\[(4a^b)^c = 4^ca^{bc}\] (power or a power rule)
So the LHS can be rewritten as:
\[a^b(4a^b)^c = a^b \times 4^ca^{bc} = 4^c a^{bc+b} \]

Now the RHS is \[1024a^{6b}\]

If you compare the LHS with RHS you should see that you have two parts, the power of 4 and the power of a:



So we can match the 4^c with 1024 and the a^(bc+b) with a^6b
\[4^c = 1024; a^{bc+b} = a^{6b}\]

Solve for c, and then plug into the equation with a and you can find b.