Question
Simplify the following:
$\frac{6(8)^{\text{n}+1}+16(2)^{3\text{n}-2}}{10(2)^{3\text{n}+1}-7(8)^\text{n}}$
$\frac{6(8)^{\text{n}+1}+16(2)^{3\text{n}-2}}{10(2)^{3\text{n}+1}-7(8)^\text{n}}$
✓
Answer
$\frac{(6\times8^{\text{n}+1})+(16\times2^{3\text{n}-2})^{}}{(10\times2^{3\text{n}+1})-7\times(8)^{\text{n}}}$
$=\frac{(6\times8^\text{n}\times8)+(16\times8^\text{n}\times\frac{1}{4})}{(10\times8^\text{n}\times2)-7\times(8)^\text{n}}$
$=\frac{8^\text{n}(48+4)}{8^\text{n}(20-7)}$
$=\frac{52}{13}=4$
$=\frac{(6\times8^\text{n}\times8)+(16\times8^\text{n}\times\frac{1}{4})}{(10\times8^\text{n}\times2)-7\times(8)^\text{n}}$
$=\frac{8^\text{n}(48+4)}{8^\text{n}(20-7)}$
$=\frac{52}{13}=4$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Using factor theorem, show that $g(x)$ is a factor of $p(x),$ when
$p(x) = x^3 - 8, g(x) = x - 2$
→$p(x) = x^3 - 8, g(x) = x - 2$
Find the mode for the following series:
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2
Classify the number 0.3796 as rational or irrational.
The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
Following are the weights of 10 new born babies in a hospital on a particular day:
3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6 (in kg). Find the mean $\overline{\text{X}}.$
→3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6 (in kg). Find the mean $\overline{\text{X}}.$
Evaluate: $25^3 - 75^3 + 50^3$
→Define the following terms:
Line segment.
Line segment.
Fig.,$ AB || CD$ and $CD || EF$. Also$, EA \perp AB.$ If $\angle BEF = 55^\circ ,$ find the values of $x, y,$ and $z$.
→Simplify the following expression : $(\sqrt{3}+\sqrt{7})^2$
→Evaluate:
$\frac{2^0+7^0}{5^0}$
→$\frac{2^0+7^0}{5^0}$