+218 Please find the original thread, and answer here: https://web2.0calc.com/questions/manipulating-exponents
Melody the question I wrote was wrong. It was actually:
Write 427(23+m3+2m3)3as a power of 2.
+118696 Thanks Mathy.
Now it comes out perfectly well.
If you still need help with it please put this correct version, along with the explantatory note, on the original thread.
I can help you over there is you still want me too,
+118696
427(23+m3+2m3)3=427([23+m3]+[2m3])3=427([23+m3]3+3∗[23+m3]2[2m3]+3∗[23+m3][2m3]2+[2m3]3)=427([23+m]+3∗[26+2m3][2m3]+3∗[23+m3][22m3]+[2m])=427([23+m]+3∗[26+3m3]+3∗[23+3m3]+[2m])=427([23+m]+3∗[22+m]+3∗[21+m]+[2m])=4∗2m27([23]+3∗[22]+3∗[2]+[1])=4∗2m27(8+12+6+1)=4∗2m27(27)=2(m+2)
LaTex
\frac{4}{27}\left(2^{\frac{3+m}{3}}+2^{\frac{m}{3}}\right)^3\\
=\frac{4}{27}\left( \left[ 2^{\frac{3+m}{3}} \right] + \left[ 2^{\frac{m}{3}} \right] \right)^3\\
=\frac{4}{27}\left(\left[ 2^{\frac{3+m}{3}} \right]^3
+ 3*\left[ 2^{\frac{3+m}{3}} \right]^2 \left[ 2^{\frac{m}{3}} \right]
+ 3*\left[ 2^{\frac{3+m}{3}} \right] \left[ 2^{\frac{m}{3}} \right] ^2 + \left[ 2^{\frac{m}{3}} \right] ^3 \right)\\
=\frac{4}{27}\left(\left[ 2^{3+m} \right]
+ 3*\left[ 2^{\frac{6+2m}{3}} \right] \left[ 2^{\frac{m}{3}} \right]
+ 3*\left[ 2^{\frac{3+m}{3}} \right] \left[ 2^{\frac{2m}{3}} \right] + \left[ 2^{m} \right] \right)\\
=\frac{4}{27}\left(\left[ 2^{3+m} \right]
+ 3*\left[ 2^{\frac{6+3m}{3}} \right]
+ 3*\left[ 2^{\frac{3+3m}{3}} \right] + \left[ 2^{m} \right] \right)\\
=\frac{4}{27}\left(\left[ 2^{3+m} \right]
+ 3*\left[ 2^{2+m} \right]
+ 3*\left[ 2^{1+m} \right] + \left[ 2^{m} \right] \right)\\
=\frac{4*2^m}{27}\left(\left[ 2^{3} \right]
+ 3*\left[ 2^{2} \right]
+ 3*\left[ 2 \right] + \left[ 1 \right] \right)\\
=\frac{4*2^m}{27}\left(8+ 12 + 6 + 1\right)\\
=\frac{4*2^m}{27}\left(27\right)\\
=2^{(m+2)}
