a power M by a power n is equals to a power n. by a n m with different integers​

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a power M by a power n is equals to a power n. by a n m with different integers​

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Ximena 1 month 2021-08-16T07:16:00+00:00 2 Answers 0 views 0

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    2021-08-16T07:17:01+00:00

    Answer:

    good morning sis in which class do you study

    0
    2021-08-16T07:17:27+00:00

    First let’s look at how to work with variables to a given power, such as a3.

    There are five rules for working with exponents:

    1. am * an = a(m+n)

    2. (a * b)n = an * bn

    3. (am)n = a(m * n)

    4. am / an = a(m-n)

    5. (a/b)n = an / bn

    Let’s look at each of these in detail.

    1. am * an = a(m+n) says that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it’s the same as taking that number a and raising it to a power equal to the sum of m + n.

    Here’s an example where

    a = 3

    m = 4

    n = 5

    am * an = a(m+n)

    34 * 35 = 3(4+5) = 39 = 19,683

    2. (a * b)n = an * bn says that when you multiply two numbers, and then multiply that product by itself n times, it’s the same as multiplying the first number by itself n times and multiplying that by the second number multiplied by itself n times.

    Let’s work out an example where

    a = 3

    b = 6

    n = 5

    (a * b)n = an * bn

    (3 * 6)5 = 35 * 65

    185 = 35 * 65 = 243 * 7,776 = 1,889,568

    3. (am)n = a(m * n) says that when you take a number, a , and multiply it by itself m times, then multiply that product by itself n times, it’s the same as multiplying the number a by itself m * n times.

    Let’s work out an example where

    a = 3

    m = 4

    n = 5

    (am)n = a(m * n)

    (34)5 = 3(4 * 5) = 320 = 3,486,784,401

    4. am / an = a(m-n) says that when you take a number, a, and multiply it by itself m times, then divide that product by a multiplied by itself n times, it’s the same as a multiplied by itself m-n times.

    Here’s an example where

    a = 3

    m = 4

    n = 5

    am / an = a(m-n)

    34 / 35 = 3(4-5) = 3-1 (Remember how to raise a number to a negative exponent.)

    34 / 35 = 1 / 31 = 1/3

    5. (a/b)n = an / bn says that when you divide a number, a by another number, b, and then multiply that quotient by itself n times, it is the same as multiplying the number by itself n times and then dividing that product by the number b multiplied by itself n times.

    Let’s work out an example where

    a = 3

    b = 6

    n = 5

    (a/b)n = an / bn

    (3/6)5 = 35 / 65

    Remember 3/6 can be reduced to 1/2. So we have:

    (1/2)5 = 243 / 7,776 = 0.03125

    Understanding exponents will prepare you to use logarithms

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