Question

3. Simplify: :
4^3n+4^2n. 4^n+1/
(4 x 4^n) ^3- 4 x 4^3n
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Answer 1

Answer:

$\mathrm{\frac{4^3n+4^2n\times \:4^n+1}{\left(4\times \:4^n\right)^3-4\times \:4^3n}=\frac{64n+4^{2+n}n+1}{64^{1+n}-256n}}$

Step-by-step explanation:

$\mathrm{\frac{4^3n+4^2n\times \:4^n+1}{\left(4\times \:4^n\right)^3-4\times \:4^3n}}$

$\mathrm{=\frac{64n+4^{n+2}n+1}{\left(4\times \:4^n\right)^3-4^3\times \:4n}}$

$=\mathrm{\frac{64n+4^{n+2}n+1}{\left(4^{n+1}\right)^3-256n}}$

$\mathrm{Apply\:exponent\:rule:\quad \left(a^b\right)^c=a^{bc}}$

$\mathrm{=\frac{64n+4^{n+2}n+1}{4^{3\left(n+1\right)}-256n}}$

$\mathrm{=\frac{64n+4^{n+2}n+1}{64^{n+1}-256n}}$