How do you multiply ${(54)}^{68} \cdot {(- 13)}^{66}$ $(54) ^ { 68} \cdot ( - 13) ^ { 66}$ ?

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Answer 1 · 2018-01-16T10:45:29

Use a calculator. There's no shortcut.

Answer 2 · 2018-01-16T12:51:30

$2.1039 \times 10^{191}$ $2.1039×10^191$

I tried to use the calculator and is impossible due to the calculator limits.

let's use logarithms

I will use log as log base 10.

${(54)}^{68} \cdot {(- 13)}^{66} = {(54)}^{68} \cdot {(13)}^{66}$ $(54)^68⋅(−13)^66=(54)^68⋅(13)^66$

$log ({(54)}^{68} \cdot {(13)}^{66}) = 68 log 54 + 66 log 13$ $log((54)^68⋅(13)^66)=68 log 54 +66 log13$

117.8027757+73.52026125=191.323037

The resusult will be $10^{191.323037} = 10^{191} \times 10^{0.323037} = 2.1039 \times 10^{191}$ $10^191.323037=10^191xx10^0.323037=2.1039xx10^191$

How do you multiply (54)68⋅(−13)66(54) ^ { 68} \cdot ( - 13) ^ { 66}?