Lesson 2: Multiplying and Dividing Power

This week, I have learned how to multiply and divide powers and how to solve negative exponent. It took time to understand but practicing many times lead me to get better.

Multiply Powers

When multiplying powers we must first learn some vocabularies, such as powerbase, and exponent.

The power is a number written in exponential form.

  • Example: {2^3}. This is a power.

base and the exponent consists in the power

  • Example: {2^3}. The 2 would be the base and the exponent would be the 3.

Now we know the vocabularies, so we can learn further.

We will start from the basics by having the same base.

To multiply 2 different powers, we must first identify the exponent from both sides.

  • Exemple {2^3} x {2^2}

For the first power, we have 3 as the exponent, and in the second power, we have 2 as the exponent. Here, we can do the calculation.

First you take both exponent, so it will be 3 and 2, then you add both of them. But you don’t add the base.

  • Example:{2^3} x {2^2}   3+2=5

You should end with {2^5} since you will leave the base alone.

When calculation is multiplication, you add the exponent, then you multiply the base.

  • Exemple {2^3} x {4^2}       2×4=8      3+2=5       {8^5}

As a result, it will equal to {8^5}.

 

Divide Powers

To divide powers, you take the same step as multiplying powers, but you subtract instead of adding the exponent.

First you take the exponent, then you subtract from each.

  • {8^5}{8^2}  5-2=3

For this solution, we will have {8^3}.

Now let’s calculate the base. We will follow the same steps but now, we divide the bases.

  • Example: {8^5}{4^2}      8/4=2      5-2=3

As a result, we will have {2^3} since we divide 8 by 4, then subtracted 2 from 5.

 

Negative Exponents

In this image we have {3x^-2}.

When you have a negative exponent, (the first step) is to flip the whole number to a fraction form. The denominator is always 1 and numerator is whole number.

whole number is a number without fractions; an integer.

The next step is to take off the negative sign on the 2 and place the whole number and variables as denominator with 1 in numerator.

Then in order to take off the bracket, you put an exponent “2” on each base. If it is a different exponent like 3, you would put 3 on each base.

Then you multiply the whole number and variables 2 times because the exponent is 2.

As a result, your answer is 1 in numerator and 9×2 in denominator.

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