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Add the exponents

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Q: When you are multiplying exponents do you only add the exponents or do you also multiply the bases?

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Exponents are higher in priority in terms of the order of operations, and do not combine in the same way as you would simple add/subtract/multiply/divide. So, if you have: 26 + 24 This is a polynomial in base 2 with different powers. It would be this in binary: 1010000 ...which would not be the same as 210: 1000000000 In order to be able to change exponents, you have to be multiplying factors using the same base, as in: 26 * 24 = 210 ...because the exponents are also indicating how many times you are multiplying each base by itself, and multiplication is the same as the basal function of the exponent (repeated multiplication).

To understand this, you have to think about what an exponent represents. An exponent is a representation of the number of times the base is multiplied by itself. For example: a3 = a × a × a or: a5 = a × a × a × a × a now look at those same two examples, and consider what happens when you multiply them together: a3 × a5 = (a × a × a) × (a × a × a × a × a) The order of operations doesn't matter in this case, as they're all using the same operator. That means we can get rid of those brackets: = a × a × a × a × a × a × a × a = a8 The exponents are multiplied when a term is raised to more than one power. For example: (a2)3 can also be expressed as: (a2) × (a2) × (a2) = (a × a) × (a × a) × (a × a) = a × a × a × a × a × a = a6

Multiplication is nothing but repeated addition.We multiply whole numbers by referring to their multiplication tables and also by multiplying first the layer digit, then carrying off and then multiplying all the digits successively.

To simplify, you write one copy of the base, then add the exponent. Example:x^5 times x^3 = x^8 In the case of positive integer exponents, this can easily be derived by writing each power as a repeated multiplication. However, this law is also valid for negative or fractional exponents.

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You have to add the exponents. It's best if you just remember it. You can also consider what happens when you multiply something like:(2 x 2 x 2) x (2 x 2) As you can notice, the number of factors get added. That's like adding the exponents.

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Exponents are higher in priority in terms of the order of operations, and do not combine in the same way as you would simple add/subtract/multiply/divide. So, if you have: 26 + 24 This is a polynomial in base 2 with different powers. It would be this in binary: 1010000 ...which would not be the same as 210: 1000000000 In order to be able to change exponents, you have to be multiplying factors using the same base, as in: 26 * 24 = 210 ...because the exponents are also indicating how many times you are multiplying each base by itself, and multiplication is the same as the basal function of the exponent (repeated multiplication).

To understand this, you have to think about what an exponent represents. An exponent is a representation of the number of times the base is multiplied by itself. For example: a3 = a × a × a or: a5 = a × a × a × a × a now look at those same two examples, and consider what happens when you multiply them together: a3 × a5 = (a × a × a) × (a × a × a × a × a) The order of operations doesn't matter in this case, as they're all using the same operator. That means we can get rid of those brackets: = a × a × a × a × a × a × a × a = a8 The exponents are multiplied when a term is raised to more than one power. For example: (a2)3 can also be expressed as: (a2) × (a2) × (a2) = (a × a) × (a × a) × (a × a) = a × a × a × a × a × a = a6

Multiplication is nothing but repeated addition.We multiply whole numbers by referring to their multiplication tables and also by multiplying first the layer digit, then carrying off and then multiplying all the digits successively.

To simplify, you write one copy of the base, then add the exponent. Example:x^5 times x^3 = x^8 In the case of positive integer exponents, this can easily be derived by writing each power as a repeated multiplication. However, this law is also valid for negative or fractional exponents.

0.01 is also written as 1*10^(-2), (1*10^-2)^10=1*10^(-2*10), since raising exponents by to other powers is the same as multiplying the exponents together. The result is 1*10^(-20) or 0.00000000000000000001 (nineteen zeros after the decimal point).

One use is shorthand for large numbers, eg the mass of the earth is 5960000000000000000000000 kg , which can be expressed as: 5.96 * 1024 kg there are also rules for multiplying / dividing exponential numbers

0.000000001 is equal to one billionth, or 10-9. A kilometer is 103 meters. When multiplying exponents, add them together. In this case, we get 10-6, or one millionth of a meter - which can also be expressed as 0.000001.

If the bases are the same then just do simple exponent addition just add hte exponents eg 2 to the power of 5 + 2 to the power of 3 = 2 to the power of 5+3 =2 to the power of 8 this can also be simplified to 1 to the power of 4

If you multiply a number by 100%, you are simply multiplying by 1. You can multiply by 100% to change a decimal number or fraction to a percent. (0.25)(100%)=25%. You can also divide by 100% to change a percent to a decimal number. 65%/100%= 65/100 or 0.65.

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