"To the power of" (powers in division have to be subtracted)

[PeroK]

I was introduced but was nt sure were they can be used or sometimes forget the mechanisim.

One of the reasons that this notation is useful is that many of the natural constants and quantities are either very large or very small in SI units. In physics, we have things like:

The mass of an electron is $9.1 \times 10^{-31} kg$; and the mass of the Sun is $2 \times 10^{30}kg$.

It would be very confusing to write these out with a long line of thirty zeroes.

 

[chriscarson]

You could also note that it's consistent with the properties you already know. $x^n x^{-n} = x^{n-n} = x^0 = 1$, so divide through by $x^n$ and you see $x^{-n} = \frac{1}{x^n}$.

But N.B. AFAIK $x^0 := 1$ and $x^{-n} := \frac{1}{x^n}$ are definitions, and the exponent laws can be proven by induction. So the first sentence is deriving it backwards

you have to know these things well before try to solve this sums. i ll see how it goes with my next work . thanks

 

[chriscarson]

One of the reasons that this notation is useful is that many of the natural constants and quantities are either very large or very small in SI units. In physics, we have things like:

The mass of an electron is $9.1 \times 10^{-31} kg$; and the mass of the Sun is $2 \times 10^{30}kg$.

It would be very confusing to write these out with a long line of thirty zeroes. and you can see the digits how

that what standard form are used for from what I see. from an electron to the sun there is an outstanding gap of size but still, the can be written in a little amount of digits.

 

[Delta2]

I was introduced but was nt sure were they can be used or sometimes forget the mechanisim.

It is important to notice that the equation $$10^n\cdot 10^m=10^{n+m}$$ holds even when m and n are negative numbers (or when one of n, m is negative and the other positive). For example $$\frac{10^3}{10^5}=10^3\cdot 10^{-5}=10^{3+(-5)}=10^{-2}=\frac{1}{10^2}$$

 

[etotheipi]

Plus there is a natural correspondence between the naming system and the standard form, e.g. two nonillion, nine hundred and eleven decillionths?

Also

 

[chriscarson]

It is important to notice that the equation $$10^n\cdot 10^m=10^{n+m}$$ holds even when m and n are negative numbers (or when one of n, m is negative and the other positive). For example $$\frac{10^3}{10^5}=10^3\cdot 10^{-5}=10^{3+(-5)}=10^{-2}=\frac{1}{10^2}$$

ok so it comes to play the knowledge about the order operations or bidmas then

 

[chriscarson]

Plus there is a natural correspondence between the naming system and the standard form, e.g. two nonillion, nine hundred and eleven decillionths?

Also

wow this hurts your mind lol , was minecraft world a joke outside in the universe?

 

[etotheipi]

wow this hurts your mind lol , was minecraft world a joke outside in the universe?

LOL, I hadn't noticed that part. It's been a very long time since I last played that . Apparently it's something like 64,000 km wide and contains about 130 quadrillion blocks...

By the way this is the original, an interactive version.

 

[chriscarson]

LOL, I hadn't noticed that part. It's been a very long time since I last played that . Apparently it's something like 64,000 km wide and contains about 130 quadrillion blocks...

By the way this is the original, an interactive version.

this is better you can stare to minecraft world lol

 

[Delta2]

ok so it comes to play the knowledge about the order operations or bidmas then

Yes ofcourse, order of operations is important in order to correctly interpret the algebra, for example when i write $$10^3\cdot 10^{-5}$$ I mean $$(10^3)\cdot(10^{-5})$$ and not $$((10^3)\cdot 10)^{-5}$$. Exponentiation (whether it is to a positive or negative exponent, this doesn't matter) has bigger priority than multiplication/division or addition/subtraction. The order of operations is not always the same with the order we read from left to right.

 

[chriscarson]

Yes ofcourse, order of operations is important in order to correctly interpret the algebra, for example when i write $$10^3\cdot 10^{-5}$$ I mean $$(10^3)\cdot(10^{-5})$$ and not $$((10^3)\cdot 10)^{-5}$$. Exponentiation (whether it is to a positive or negative exponent, this doesn't matter) has bigger priority than multiplication/division or addition/subtraction. The order of operations is not always the same with the order we read from left to right.

exactly as BIDMAS say and call them indices

 

[Delta2]

exactly as BIDMAS say and call them indices

Yes ok I guess you can call exponents indices but usually I call indices the "lower" indices for example when i write $$a_1^2+x=0$$ the 1 is the lower index (or just index) and is used to denote the specific variable $a_1$, while 2 is the upper index or the exponent and it corresponds to the mathematical operation "to the power of". It is $$a_1^2=(a_1)\cdot (a_1)$$

 

[chriscarson]

Yes ok I guess you can call exponents indices but usually I call indices the "lower" indices for example when i write $$a_1^2+x=0$$ the 1 is the lower index (or just index) and is used to denote the specific variable $a_1$, while 2 is the upper index or the exponent and it corresponds to the mathematical operation "to the power of".

I see ,so they get more complicated with the lower indices.

 

[chriscarson]

I met something else I can t solve because something new , I mean every step is something new ,the answer have to be 3 to the power of 4

 

[PeroK]

I met something else I can t solve because something new , I mean every step is something new ,the answer have to be 3 to the power of 4View attachment 265362

The first step is not right. What is $9 \times 3^2$ equal to?

And, big hint here, what is $3 \times 27$ equal to?

 

[chriscarson]

The first step is not right. What is $9 \times 3^2$ equal to?

And, big hint here, what is $3 \times 27$ equal to?

The first step is not right. What is $9 \times 3^2$ equal to?

And, big hint here, what is $3 \times 27$ equal to?

3x3 is 9 and 9x9 is 81

 

[PeroK]

3x3 is 9 and 9x9 is 81

Yes. And $3 \times 27$?

 

[chriscarson]

Yes. And $3 \times 27$?

also 81

 

[PeroK]

also 81

Does that help?

 

[chriscarson]

Does that help?

81 to the power of 3 divided by 81 to the power of 2 for me is 81 to the power of 1 , the answer is 3 to the power of 4

 

[PeroK]

81 to the power of 3 divided by 81 to the power of 2 for me is 81 to the power of 1 , the answer is 3 to the power of 4

What's the difference between $81$ and $3^4$?

 

[chriscarson]

What's the difference between $81$ and $3^4$?

nothing but I understand it now that you asked it .so you have to dissolve indices and then create it again for the answer? what about when they have different bases like 64² diveded by 16³ ? my result was 4^-1

 

[PeroK]

nothing but I understand it now that you asked it .so you have to dissolve indices and then create it again for the answer? what about when they have different bases like 64² diveded by 16³ ? my result was 4^-1

An answer of $81$ is just as good as an answer of $3^4$.

 

[chriscarson]

An answer of $81$ is just as good as an answer of $3^4$.

ok thanks

 

[Mark44]

what about when they have different bases like 64² diveded by 16³ ? my result was 4^-1

No.
$$\frac {64^2}{16^3} = \frac {4^2 16^2}{16^3} \ne \frac 1 4$$

It would be good for you to learn and memorize the basic properties of exponents such as
$(ab)^n = a^nb^n$
$a^ma^n = a^{m + n}$
$\frac {a^m}{a^n} = a^{m - n}$
There are a few more.

 

[chriscarson]

No.
$$\frac {64^2}{16^3} = \frac {4^2 16^2}{16^3} \ne \frac 1 4$$

It would be good for you to learn and memorize the basic properties of exponents such as
$(ab)^n = a^nb^n$
$a^ma^n = a^{m + n}$
$\frac {a^m}{a^n} = a^{m - n}$
There are a few more.

https://www.matesfacil.com/english/secondary/solved-exercises-powers.htmlAfter all this time it sow that I found something with numbers and not letters to understand more . In the bottom link . Thanks I will get help with yours too.