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arbre
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compare the size of different order roots. 31 May 2022, 01:43
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What is the reason behinds We can also compare the size of different order roots.
.eg,0<b<1 ,m<n, the Mth root of b is smaller then the Nth root of b
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avigutman
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compare the size of different order roots. 31 May 2022, 05:55
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arbre
What is the reason behinds We can also compare the size of different order roots.
.eg,0<b<1 ,m<n, the Mth root of b is smaller then the Nth root of b
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Exponents and roots describe a repetitive multiplicative relationship of a base number with itself.
For example, 3^4 = 3*3*3*3, and (1/4)^5 = (1/4)*(1/4)*(1/4)*(1/4)*(1/4)
Now, with a positive base repetitively multiplied times itself, you're going to go farther and farther away from zero if that base is greater than 1 (because you keep multiplying by a factor that is greater than 1), and you're going closer and closer to zero if that base is between 0 and 1 (because you keep multiplying by a fraction).
Roots are the reverse operation of exponents, so their effect on the number line (going farther from or closer to zero) is the exact opposite of the exponents' effect.
Does that answer your question, arbre?
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arbre
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compare the size of different order roots. 04 Jun 2022, 21:48
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Roots are the reverse operation of exponents, so their effect on the number line (going farther from or closer to zero) is the exact opposite of the exponents' effect.
Does that answer your question, arbre?[/quote]


i dont quite understand why ? would you mind tell me a bit more? thanks!
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compare the size of different order roots. 05 Jun 2022, 05:13
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arbre what exactly is your question? Why roots are the reverse operation of exponents?

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compare the size of different order roots. 05 Jun 2022, 23:05
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arbre
What is the reason behinds We can also compare the size of different order roots.
.eg,0<b<1 ,m<n, the Mth root of b is smaller then the Nth root of b

Exponents and roots describe a repetitive multiplicative relationship of a base number with itself.
For example, 3^4 = 3*3*3*3, and (1/4)^5 = (1/4)*(1/4)*(1/4)*(1/4)*(1/4)
Now, with a positive base repetitively multiplied times itself, you're going to go farther and farther away from zero if that base is greater than 1 (because you keep multiplying by a factor that is greater than 1), and you're going closer and closer to zero if that base is between 0 and 1 (because you keep multiplying by a fraction).
[color=#ffff00][color=#ff0000]Roots are the reverse operation of exponents[/color][color=#ff0000][/color][/color], so their effect on the number line (going farther from or closer to zero) is the exact opposite of the exponents' effect.
Does that answer your question, arbre?
Show more

hi, i am refer to this part (please see in the bold and underlined part)
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avigutman
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compare the size of different order roots. 06 Jun 2022, 15:39
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arbre
avigutman
Roots are the reverse operation of exponents
I dont quite understand why ? would you mind tell me a bit more? thanks!
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arbre In the same way that division is the reverse operation of multiplication, and addition is the reverse operation of subtraction.
So, for example, if it's true that 3^3 = 27 (in other words, 3*3*3 = 27), then it's true that the cube root of 27 is 3.