Question

What is the simplified expression for 6^4.6^3 over 6^5 6^1 6^2 6^3 6^7

Answer 1

Answer:

6^2

Step-by-step explanation:

Question:-

• To simplify the given expression

Expression:-

• $\frac{ {6}^{4} . {6}^{3} }{ {6}^{5} }$

Solution:-

$= \frac{ {6}^{4} . {6}^{3} }{ {6}^{5} }$

• [As we know, a^x . a^y = a^(x+y)]

$= \frac{ {6}^{(4 + 3)} }{ {6}^{5} }$

• [On Simplification]

$= \frac{ {6}^{7} }{ {6}^{5} }$

• [As we know, a^x / a^y = a^(x-y)]

$= {6}^{(7 - 5)}$

• [On Simplification]

$= {6}^{2} (ans)$

Answer 2

$\bf\huge Question:—$

$\bf \: 6^4.6^3 \: over \: {6}^{5}$

$\bf\huge Solution:—$

$\sf\longmapsto \: \dfrac{6^4.6^3}{ {6}^{5} }$

$\boxed{\bf \: Note \: that \: '.' \: sign = \times}$

$\sf\longmapsto \dfrac{6^4 \times 6^3}{ {6}^{5} }$

$\sf\longmapsto \: \dfrac{ \cancel6^4 \times 6^3}{ \cancel{6}^{5} }$

$\boxed{\bf \: Cancel\: 6^4\: and \:6^5 , ans\: is\: 6^1.}$

$\sf\longmapsto \: \dfrac{ {6}^{3} }{ {6}^{1} }$

$\boxed{\bf \: Simply\: subtract\: 3-1 \: as \: \: a^n/a^n \: = \: a^{n-n} \: .}$

$\sf\longmapsto \: 6 {}^{3 - 1}$

$\sf\longmapsto6 {}^{2}$

________________________________

$\boxed{\bf Solving\: In \: Another \: Way}$

$\sf\longmapsto \dfrac{1296( {6}^{3} )}{6 {}^{5} }$

$\sf\longmapsto \: \dfrac{1296(216)}{ {6}^{5} }$

$\sf\longmapsto \: \dfrac{279936}{ {6}^{5} }$

$\sf\longmapsto \: \dfrac{279936}{7776}$

$\sf\longmapsto \: \cancel \dfrac{279936}{7776}$

$\sf\longmapsto36$

$\boxed{\bf Now \:Convert \:36\: to \:exponent}$

$\sf\longmapsto 36$

$\sf\longmapsto 6^2(6×6)$

$\sf\longmapsto {6}^{2}$

________________________________

$\boxed{ \bf \: Answer \: is \: Option \: A }$

$\boxed{ \bf \: {6}^{2} }$