Summing Powers

Algebra Level 1

$\large \frac{4^{5} + 4^{5} + 4^{5} + 4^{5}}{ 3^{5} + 3^{5} + 3^{5}} \times \frac{ 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5}}{2^{5} + 2^{5}} = \text{?}$

2^{11}

2^{10}

2^{6}

2^{12}

3 solutions

Sakanksha Deo
Mar 9, 2015

$\frac{4^{5} + 4^{5} + 4^{5} + 4^{5}}{ 3^{5} + 3^{5} + 3^{5}} \times \frac{ 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5}}{2^{5} + 2^{5}}$

$= \frac{ 4\times 4^{5} }{ 3\times 3^{5} } \times \frac{ 6\times 6^{5} }{ 2\times 2^{2} }$

$= \frac{ 4^{6} }{ 3^{6} } \times \frac{ 6^{6} }{ 2^{6} }$

$= [ \frac{4}{3} \times \frac{6}{2} ]^{6}$

$= ( 4 )^{6} = ( 2^{2} )^{6} = \boxed{ 2^{12} }$

Good Work @Sakanksha Deo!

Just a side note : Insert your math equations in "\ [ .... \ ]" to make them stand out (for better display results). Use "\ ( ... \ )" when you want to insert inline maths.

Kishlaya Jaiswal - 6 years, 3 months ago

Thanx for the advice.... :)

Sakanksha Deo - 6 years, 3 months ago

ALSO use can use \dfrac{..}{...} rather than \frac{...}{...} for increasing size of the fraction $\ddot\smile$

Parth Lohomi - 6 years, 3 months ago

@Parth Lohomi – Thanx....will use that in future..

Sakanksha Deo - 6 years, 3 months ago

Caleb Townsend
Mar 8, 2015

$x = \frac{4\times 4^5}{3\times 3^5}\times \frac{6\times 6^5}{2\times 2^5}$ $x = \frac{4^6}{2^6}\times \frac{6^6}{3^6}$ $x = 2^6 \times 2^6 = \boxed{2^{12}}$

Ernesto L. Raz Jr.
Mar 19, 2015

I response to Caleb Townsend Very Nice :)

Summing Powers

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