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MATH REVIEW: helpful MATH because that EVERYONE

SECTION 3.2. WHAT IS one EXPONENT?

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First let"s look at at exactly how to job-related with variables come a given power, such as a3.

You are watching: To multiply a number by itself

There are 5 rules because that working with exponents:

1. To be * 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 at each of these in detail.

1. am * an = a(m+n) claims that as soon as you take it a number, a, multiply by chin m times, and multiply that by the very same number a multiply by chin n times, it"s the same as acquisition that number a and raising it come a strength equal come the sum of m + n.

Here"s an example where

a = 3 m = 4 n = 5

am * one = a(m+n)

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

2. (a * b)n = one * bn claims that once you multiply two numbers, and then multiply the product by itself n times, it"s the very same as multiplying the an initial number by itself n times and multiplying the by the 2nd number multiplied by chin n times.

Let"s work-related 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 once you take a number, a , and multiply it by itself m times, climate multiply the product by chin n times, it"s the exact same as multiplying the number a by itself m * n times.

Let"s occupational out an instance 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) claims that as soon as you take it a number, a, and multiply that by itself m times, then division that product by a multiply by chin n times, it"s the exact same as a multiply by itself m-n times.

Here"s an instance where

a = 3 m = 4 n = 5

am / an = a(m-n)

34 / 35 = 3(4-5) = 3-1 (Remember exactly how to advanced a number come a an adverse exponent.)

34 / 35 = 1 / 31 = 1/3

5. (a/b)n = an / bn claims that once you divide a number, a by another number, b, and also then multiply the quotient by itself n times, it is the same as multiplying the number by itself n times and then splitting that product by the number b multiply by chin n times.

Let"s work out an instance where

a = 3 b = 6 n = 5

(a/b)n = an / bn

(3/6)5 = 35 / 65

Remember 3/6 can be lessened to 1/2. So us have:

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

Understanding exponents will certainly prepare you to usage logarithms.

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