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This lesson is a continuation from part 1 of the Exponent Laws.

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To emphasize, it is very important to understand the logic behind these laws before you use them.

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The laws that you are going to learn can be derived from the first three laws in part 1. So, they are not completely new.

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Let's start, consider this term, bracket 2 multiply by 3 , to the power of 4.

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Now, we can break this term into four parts of bracket 2 multiply by 3.

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We can see that 2 multiply by 2, multiply by 2, multiply by 2, gives 2 power of 4.

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Similarly, 3 multiply by 3, multiply by 3, multiply by 3, gives 3 power of 4

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Now, notice this, this term bracket 2 multiply by 3 to the power of 4 is equals to, 2 to the power of 4 multiply by 3 to the power of 4.

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With this observation, we can now formulate an exponent law.

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Let's first replace these numbers with alphabetical letters. This gives bracket 'a' multiply by 'b' to the power of n.

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By referring to this, we can also see this term, bracket 'a' multiply by 'b' to the power of N is equals to, 'a' to the power of 'n' multiply by 'b' to the power of n.

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So, we have another law of exponent. Bracket 'a' multiply 'b' to the power of 'n' is equals to, 'a' to the power of 'n' multiply b' to the power of 'n'.

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Let's take a look at the next law of exponent. For us to understand this law, let's consider dividing 2 to the power of 3 with 2 to the power of 3.

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Now, using the second exponent law, we can see that, this term is equals to, 2 to the power of 3 minus 3.

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Three minus by three is 0. So, now we have 2 to the power of 0.

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Alright, let's calculate this term using another way. We can see that 2 to the power of 3 divides by 2 to the power of 3 is equals to, 8 divides by 8.

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Now, 8 divides by 8 gives 1.

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From here, we can see something interesting. Since all these terms are equal to each other, we can say that, 2 to the power of zero is equals to 1.

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With this observation, we can now formulate an exponent law.

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Let's first replace this number, '2' with 'a'. This gives 'a' to the power of zero.

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By referring to this, we can deduce that, 'a' to the power of zero is equal to 1.

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So, here we have another law of exponents. 'a' to the power of zero equals to 1.

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Let's take a look at the next law of exponent. For us to understand this law, let's consider this term, 1 divides by 2 to the power of 3.

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Now, notice the number 1, at the numerator. Using this exponent law, 'a' to the power of zero equals to 1, we can rewrite 1 as, 2 to the power of 0.

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Now, using the second law of exponents, 2 to the power of 0 divides by two to the power of 3 is equals to, 2 to the power of 0 minus 3.

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0 minus 3 gives negative 3. So now we have, 2 to the power of negative 3.

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Again, we can see something interesting. If we observe carefully, since all these terms are equal, we can see that 2 to the power of negative 3 is equals to 1 divides by 2 to the power of 3.

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Let's rewrite these two terms here.

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With this observation, we can now formulate an exponent law.

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Let's first replace these numbers with alphabetical letters. This gives 'a' to the power of negative 'n'.

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By referring to this, we can deduce that, 'a' to the power of negative 'n' is equals to, 1 divides by 'a' to the power of 'n'.

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Finally, we have another law of exponents. 'a' to the power of negative 'n' equals 1 divides 'a' to the power of 'n'.

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That is all for this lesson. The next lesson will show you some examples on using what you have learn in this lesson.