The exponent of a number says how numerous times to usage the number in a multiplication.

You are watching: X 1 2 times x 2

In this example: 82 = 8 × 8 = 64

So, as soon as in doubt, just remember to compose down every the letters (as plenty of as the exponent tells you to) and see if you can make sense of it.

## All you require to recognize ...

The "Laws the Exponents" (also dubbed "Rules that Exponents") come native three ideas: The exponent says how many times to usage the number in a multiplication. A negative exponent means divide, because the the contrary of multiplying is dividing A spring exponent choose 1/n way to take the nth root: x(1n) = n√x

If you understand those, climate you understand exponents!

And all the laws listed below are based upon those ideas.

## Laws of Exponents

Here are the regulations (explanations follow):

Law instance
x1 = x 61 = 6
x0 = 1 70 = 1
x-1 = 1/x 4-1 = 1/4
xmxn = xm+n x2x3 = x2+3 = x5
xm/xn = xm-n x6/x2 = x6-2 = x4
(xm)n = xmn (x2)3 = x2×3 = x6
(xy)n = xnyn (xy)3 = x3y3
(x/y)n = xn/yn (x/y)2 = x2 / y2
x-n = 1/xn x-3 = 1/x3
And the law about Fractional Exponents:
xm/n = n√xm =(n√x )m x2/3 = 3√x2 =(3√x )2

## Laws Explained

The very first three laws above (x1 = x, x0 = 1 and also x-1 = 1/x) space just part of the organic sequence of exponents. Have a look at this:

Example: powers of 5
.. Etc.. 52 1 × 5 × 5 25
51 1 × 5 5
50 1 1
5-1 1 ÷ 5 0.2
5-2 1 ÷ 5 ÷ 5 0.04
.. Etc..

Look at the table because that a when ... Notification that positive, zero or negative exponents room really component of the same pattern, i.e. 5 times larger (or 5 times smaller) depending upon whether the exponent gets larger (or smaller).

## The law that xmxn = xm+n

With xmxn, how many times perform we end up multiplying "x"? Answer: very first "m" times, climate by another "n" times, because that a complete of "m+n" times.

### Example: x2x3 = (xx)(xxx) = xxxxx = x5

So, x2x3 = x(2+3) = x5

## The regulation that xm/xn = xm-n

Like the previous example, how plenty of times carry out we end up multiplying "x"? Answer: "m" times, climate reduce that by "n" time (because we space dividing), because that a full of "m-n" times.

### Example: x4/x2 = (xxxx) / (xx) = xx = x2

So, x4/x2 = x(4-2) = x2

(Remember the x/x = 1, so every time you see an x "above the line" and also one "below the line" you can cancel castle out.)

This regulation can likewise show you why x0=1 :

## The legislation that (xm)n = xmn

First you main point "m" times. Then you have to carry out that "n" times, because that a full of m×n times.

### Example: (x3)4 = (xxx)4 = (xxx)(xxx)(xxx)(xxx) = xxxxxxxxxxxx = x12

So (x3)4 = x3×4 = x12

## The regulation that (xy)n = xnyn

To show how this one works, just think that re-arranging all the "x"s and "y"s as in this example:

## The law that (x/y)n = xn/yn

Similar to the previous example, just re-arrange the "x"s and "y"s

## The regulation that xm/n = n√xm =(n√x )m

OK, this one is a little more complicated!

I indicate you check out Fractional index number first, so this makes much more sense.

Anyway, the vital idea is that:

x1/n = The n-th source of x

And so a fractional exponent like 43/2 is yes, really saying to execute a cube (3) and a square root (1/2), in any kind of order.

Just remember native fractions that m/n = m × (1/n):

### Example: x(mn) = x(m × 1n) = (xm)1/n = n√xm

The bespeak does not matter, for this reason it additionally works because that m/n = (1/n) × m:

## Exponents of index number ...

What around this example?

432

We do the exponent in ~ the top first, so us calculate that this way:

## And that Is It!

If you discover it hard to remember all these rules, then remember this:

you have the right to work lock out as soon as you recognize thethree ideas near the height of this page:

The exponent claims how many times to use the number in a multiplicationA negative exponent means divideA spring exponent choose 1/n way to take the nth root: x(1n) = n√x

### Oh, One more Thing ... What if x = 0?

 Positive Exponent (n>0) 0n = 0 Negative Exponent (n-n is undefined (because splitting by 0 is undefined) Exponent = 0 00 ... Ummm ... See below!

### The Strange instance of 00

There room different arguments for the correct value of 00

00 can be 1, or maybe 0, so some world say the is really "indeterminate": x0 = 1, so ... 00 = 1 0n = 0, therefore ...See more: 2000 Honda Accord 4 Cylinder Firing Order V, Diagram Of The 2002 Honda Accord Firing Order 00 = 0 When in doubt ... 00 = "indeterminate"

323, 2215, 2306, 324, 2216, 2307, 371, 2217, 2308, 2309
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