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You multiply the bases, for example, 23 x 53 = 103.
The general rule is for real numbers ( but it works for others as well) a and b
(ab)n =an bn
I think it helps to see why this is true. Look at the example given
23 is 2x2x2
53 is 5x5x5
If we multiply these we have
2x2x2x5x5x5 which is three 2's and three 5's.
Now rearrange them which we can do because of the commutative property of
multiplication and pair up each 2 with a 5 and here is what you have:
(2x5)(2x5)(2x5)
this is (2x5)3
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What are the seven rules for exponents?
Rules for exponents to multiply powers, add the exponents to divide powers, subtract the exponents to find a power of a power, multiply the exponents to find a power of a quotient, apply the power top and bottom to find a power pf a product, apply the exponent to each factor in the product x0 = 1 anything to the power zero equals one x-a = 1/xa a negative exponent means "one over" the positive exponent
How do you multiply exponets?
first you answer the exponet part. then after you get your exponet answer you multiply it with the other number. and that's how you multiply exponent's
Do you add exponents or multiply them?
Remember, all numbers have exponents, but most of the time, the exponent is 1 so we can basically ignore it. For example, 2^1 = 2. 2^2 is the same thing as 2^1 X 2^1 or 2 X 2. From this example, you can see that 2^2 = 2^(1+1). 2^3 is the same thing as 2^2 X 2^1 and so on... So, whenever you see two fractions with the same base being multiplied by each other, you add the bases. x^6 X x^3 = x^(^+3) = x^9 For division, you subtract the exponent from the top from the exponent on the bottom. x^6 ----- = x^3 x^3 -------------------------------------------------------------------------- Easy rules: Same base, multiplied, add the exponents and keep the base. EX: (x3 )(x5 ) = x8 multiplying with same base (x) so add the exponents. BUT an exponent raised to an exponent, then multiply. EX: (x3 )5 = x15 , EXPONENT RAISED OT ANOTHER EXPONENT, MULTIPLY.
What do you do when multiplying a positive exponent by a negative exponent?
Example: (4x)-2 The answer to this would be 1/ 16x2. Multiply it out as if the negative exponent was not there ((4x)2), then that will be the denominator of the fraction. The numerator is one.
What are the rules for positive integral exponent?
There are 5 laws: Product Law: This is when the same bases are being multiplied ex. 83 X 82 this is the same as 8x8x8 8x8 when the same bases are being multiplied you just add the exponents so the answer would be 85 Quotient Law: This is when the same bases are being divided. ex. 83 divided by 82 in other words 8x8x8 divided by 8x8 when the same bases are being divided you just subtract the exponents so the answer would be 81 Power of product law: here is an example : (8x3)2 in this problem all you have to do is apply the exponent to each number in side the bracket or multiply the exponent to each exponent inside the brackets, if there is no exponent you assume there is a 1 so you would do 8 1x2 and 3 1x2 and the answer would be 82x32 Power of quotient law: this is the same as the one above, you basically just multiply the exponent to the numbers inside the brackets. So if it was (8 divided by 3)4 you would assume there is an exponent 1 for both the numbers and multiply by four. 8 1x4 divided by 31x4 = 84 divided by 34 Power of a power law: What do you do if there is already an exponent inside the brackets? ex. (84)5 you would do the same thing. You multiply the exponents! if you put the question in standard form it is 8x8x8x8 repeated five times 8x8x8x8 8x8x8x8 8x8x8x8 8x8x8x8 8x8x8x8 how many 8s are there? 20 how do you solve in a much simpler way? you do 84x5 and get the 820
When an exponent to a power is multiplied by an exponent is to a different power do you multiply the powers together?
No, you add the powers together.
What is the difference between exponent and powers?
Exponent=e to the powerPower=m to the power ni.e Power=Generalized exponent
How do you get the exponent?
you get an exponent when you multiply EXAMPLE 10x10x10=1000 that is an exponent NO DONT THINK THAT IF THE EXPONENT IS 3 YOU MULTIPLY IT BY 3 NO WAY JOSE
What do you do when you multiply an exponent by a whole number?
You multiply the whole number as many times as the exponent is.
Why are numbers expressed using exponents called powers?
Because exponent is the same as power.
Evaluate the powers of 10 and a exponent of positive 4?
You evaluate the powers of 10 and a exponent of positive 4.
What happens when you multiply an exponent by another exponent?
Assuming the bases are the same, you add the exponents. 10^3 x 10^3 = 10^6
When do add exponents?
when you multiply powers with the same base.
What is the relation of the exponent rule and the power rule?
The exponent "product rule" tells us that, when multiplying two powers that The Product Rule is that when you have the same base, you can add the exponents.The quotient rule tells us that we can divide two powers with the same base by subtracting the exponents.The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56.
How do you addsubtractmultiply and divide written in scientific notation?
First you have to set it to the same power of 10. Then it can easily be added or subtracted. To multiply, you just multiply the given values and add the exponent. To divide, you divide the numbers and subtract the exponent.
What are the seven rules for exponents?
Rules for exponents to multiply powers, add the exponents to divide powers, subtract the exponents to find a power of a power, multiply the exponents to find a power of a quotient, apply the power top and bottom to find a power pf a product, apply the exponent to each factor in the product x0 = 1 anything to the power zero equals one x-a = 1/xa a negative exponent means "one over" the positive exponent
What is quotient of powers?
When you divide powers having the same base, subtract the numerator from the denomenator. Put the base in the part of the fraction where the original exponent was larger.
