+676 Well... There isn't a easy way of doing this unless there are "Special Circumstances" but... Assuming that you don't know powers, I will briefly go through it.
Powers are simply the number of times the base number is multiplied by itself.
Confusing right..? >_<
For example. 3 to the power of 5 is equal to:
$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{243}}$$
The Base number is 3 and the Index or the Power is 5.
This means 5 3's all multiplied together.!
Back to the question.
12 to the power of 27 is
$${\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}} = {\mathtt{137\,370\,551\,967\,459\,378\,662\,586\,974\,208}}$$
Nice number eh...?
But don't do it this way!
Because the Base Number (12) is the same, we can use this special method.
In terms of Indicies, multiply is the equivalent to Plus.
For example:
4 to the power of 4 Multiplied by 4 to the power of 5 is equaled to 4 to the power of 9.
Do you see what i have done here..?
Now lets go back to the question.
12 to the 27 power * 12 to the -29 power
Using the method I told you, you can just simplify it to just... 27+(-29)
This would equal to -2
Now substitute!
12 to the power of -2.
Now lets solve it!
$${{\mathtt{12}}}^{-{\mathtt{2}}} = {\frac{{\mathtt{1}}}{{\mathtt{144}}}} = {\mathtt{0.006\: \!944\: \!444\: \!444\: \!444\: \!4}}$$
Done!
REMEMBER, ONLY WORKS IF THE BASE IS THE SAME AS THE OTHER BASE!
+676 Well... There isn't a easy way of doing this unless there are "Special Circumstances" but... Assuming that you don't know powers, I will briefly go through it.
Powers are simply the number of times the base number is multiplied by itself.
Confusing right..? >_<
For example. 3 to the power of 5 is equal to:
$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{243}}$$
The Base number is 3 and the Index or the Power is 5.
This means 5 3's all multiplied together.!
Back to the question.
12 to the power of 27 is
$${\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{12}} = {\mathtt{137\,370\,551\,967\,459\,378\,662\,586\,974\,208}}$$
Nice number eh...?
But don't do it this way!
Because the Base Number (12) is the same, we can use this special method.
In terms of Indicies, multiply is the equivalent to Plus.
For example:
4 to the power of 4 Multiplied by 4 to the power of 5 is equaled to 4 to the power of 9.
Do you see what i have done here..?
Now lets go back to the question.
12 to the 27 power * 12 to the -29 power
Using the method I told you, you can just simplify it to just... 27+(-29)
This would equal to -2
Now substitute!
12 to the power of -2.
Now lets solve it!
$${{\mathtt{12}}}^{-{\mathtt{2}}} = {\frac{{\mathtt{1}}}{{\mathtt{144}}}} = {\mathtt{0.006\: \!944\: \!444\: \!444\: \!444\: \!4}}$$
Done!
REMEMBER, ONLY WORKS IF THE BASE IS THE SAME AS THE OTHER BASE!
