Exponent operations: addition, multiplication, grouping etc.
0
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I get easily confused while evaluating exponents: when should I add them and multiply them?
- We add exponents when multiplying two numbers are of the same base: i.e., $ (2^2) . (2^3) = 2^5 $ - When do we multiply exponents?
- For example: $ 2^{4^2} $ and $ (2^4)^2 $are different things. I usually resort to using a calculator or webapp to make sure I'm doing this correctly. Why can we write $ (2^4)^2 = 2^ 8$ but not $ 2^{4^2} = 2^8 $?
- When can I "group" exponents on numbers with different bases? For eg: can I write: $ (2^2) . (4^2) = (8^2) $? How about: $ sqrt{4} . sqrt{8} = sqrt{32} $?
What are other operations on exponents that I need to remember without resorting to a calculator? The first one comes naturally to me, since we can expand it out as $ 2 . 2 . 2 . 2 . 2 $. The others always evade my intuition.
linear-algebra exponentiation
asked Jan 21 at 13:26
WorldGovWorldGov
324111
$endgroup$
add a comment |
0
$begingroup$
I get easily confused while evaluating exponents: when should I add them and multiply them?
- We add exponents when multiplying two numbers are of the same base: i.e., $ (2^2) . (2^3) = 2^5 $ - When do we multiply exponents?
- For example: $ 2^{4^2} $ and $ (2^4)^2 $are different things. I usually resort to using a calculator or webapp to make sure I'm doing this correctly. Why can we write $ (2^4)^2 = 2^ 8$ but not $ 2^{4^2} = 2^8 $?
- When can I "group" exponents on numbers with different bases? For eg: can I write: $ (2^2) . (4^2) = (8^2) $? How about: $ sqrt{4} . sqrt{8} = sqrt{32} $?
What are other operations on exponents that I need to remember without resorting to a calculator? The first one comes naturally to me, since we can expand it out as $ 2 . 2 . 2 . 2 . 2 $. The others always evade my intuition.
linear-algebra exponentiation
asked Jan 21 at 13:26
WorldGovWorldGov
324111
$endgroup$
$begingroup$
$2^{4^2}$ actually represents $2^{left( 4^2right)}$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:29
$begingroup$
Also $a^c cdot b^c=(ab)^c.$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:30
add a comment |
0
0
0
$begingroup$
I get easily confused while evaluating exponents: when should I add them and multiply them?
- We add exponents when multiplying two numbers are of the same base: i.e., $ (2^2) . (2^3) = 2^5 $ - When do we multiply exponents?
- For example: $ 2^{4^2} $ and $ (2^4)^2 $are different things. I usually resort to using a calculator or webapp to make sure I'm doing this correctly. Why can we write $ (2^4)^2 = 2^ 8$ but not $ 2^{4^2} = 2^8 $?
- When can I "group" exponents on numbers with different bases? For eg: can I write: $ (2^2) . (4^2) = (8^2) $? How about: $ sqrt{4} . sqrt{8} = sqrt{32} $?
What are other operations on exponents that I need to remember without resorting to a calculator? The first one comes naturally to me, since we can expand it out as $ 2 . 2 . 2 . 2 . 2 $. The others always evade my intuition.
linear-algebra exponentiation
asked Jan 21 at 13:26
WorldGovWorldGov
324111
$endgroup$
I get easily confused while evaluating exponents: when should I add them and multiply them?
- We add exponents when multiplying two numbers are of the same base: i.e., $ (2^2) . (2^3) = 2^5 $ - When do we multiply exponents?
- For example: $ 2^{4^2} $ and $ (2^4)^2 $are different things. I usually resort to using a calculator or webapp to make sure I'm doing this correctly. Why can we write $ (2^4)^2 = 2^ 8$ but not $ 2^{4^2} = 2^8 $?
- When can I "group" exponents on numbers with different bases? For eg: can I write: $ (2^2) . (4^2) = (8^2) $? How about: $ sqrt{4} . sqrt{8} = sqrt{32} $?
What are other operations on exponents that I need to remember without resorting to a calculator? The first one comes naturally to me, since we can expand it out as $ 2 . 2 . 2 . 2 . 2 $. The others always evade my intuition.
linear-algebra exponentiation
linear-algebra exponentiation
asked Jan 21 at 13:26
WorldGovWorldGov
324111
asked Jan 21 at 13:26
WorldGovWorldGov
324111
asked Jan 21 at 13:26
WorldGovWorldGov
324111
asked Jan 21 at 13:26
WorldGovWorldGov
324111
asked Jan 21 at 13:26
WorldGovWorldGov
324111
324111
$begingroup$
$2^{4^2}$ actually represents $2^{left( 4^2right)}$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:29
$begingroup$
Also $a^c cdot b^c=(ab)^c.$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:30
add a comment |
$begingroup$
$2^{4^2}$ actually represents $2^{left( 4^2right)}$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:29
$begingroup$
Also $a^c cdot b^c=(ab)^c.$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:30
$begingroup$
$2^{4^2}$ actually represents $2^{left( 4^2right)}$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:29
$begingroup$
$2^{4^2}$ actually represents $2^{left( 4^2right)}$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:29
$begingroup$
Also $a^c cdot b^c=(ab)^c.$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:30
$begingroup$
Also $a^c cdot b^c=(ab)^c.$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:30
add a comment |
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$begingroup$
$2^{4^2}$ actually represents $2^{left( 4^2right)}$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:29
$begingroup$
Also $a^c cdot b^c=(ab)^c.$
$endgroup$
– Mohammad Zuhair Khan
Jan 21 at 13:30