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The Laws of Exponents

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**53 means the product of 3 factors of 5 = 5 x 5 x 5**

Exponents exponent Exponential Form base 53 means the product of 3 factors of 5 = 5 x 5 x 5

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**The Laws Of Exponents The laws of exponents tell us how to simplify**

expressions involving exponents. There are 7 laws of exponents.

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**Exponential form: raising a base to a power stands for**

repeated multiplication of the base times itself. n factors of x Exponential form Standard form

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**Questions What is a power? What is a base? What is exponential form?**

What is standard form? What are the laws of exponents? How many laws of exponents are there?

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**Write in exponential form.**

Write in standard form. Write in exponential form.

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**Questions Give an example of a power. Give an example of a base.**

Give an example of exponential form. Give an example of standard form.

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The Laws of Exponents:

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#1: Multiplying Bases: If you are multiplying bases with the same base, KEEP the BASE & ADD the EXPONENTS! So, I get it! When you multiply bases, you add the exponents!

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Try these:

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SOLUTIONS

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**Questions What is the first law of exponents? When can I use it?**

When can I not use it? Give an example of where I use it. Give an example of where I can’t use it. Why does it work? Give an example.

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**#3: Dividing Bases: When dividing bases with the same base, KEEP the BASE & SUBTRACT the EXPONENTS!**

So, I get it! When you divide bases, you subtract the exponents!

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Try these:

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SOLUTIONS

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**Questions What is the second law of exponents? When can I use it?**

When can I not use it? Give an example of where I use it. Give an example of where I can’t use it. Why does it work? Give an example.

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**#3: Power of a Power: If you are raising a power to a power, you multiply the exponents!**

So, when I take a Power to a power, I multiply the exponents

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Try these:

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SOLUTIONS

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**Questions What is the third law of exponents? When can I use it?**

When can I not use it? Give an example of where I use it. Give an example of where I can’t use it. Why does it work? Give an example.

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#4: Product Rule of Exponents: Raising a product to a power means raising all of the factors to the power and then multiplying. So, the power of the product is the product of the powers.

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Try these:

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SOLUTIONS

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**Questions What is the fourth law of exponents? When can I use it?**

When can I not use it? Give an example of where I use it. Give an example of where I can’t use it. Why does it work? Give an example.

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**#5: Quotient Rule of Exponents: Raising a quotient to a**

power means raising the numerator and denominator to the power. So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient.

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Try these:

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SOLUTIONS

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**Questions What is the fifth law of exponents? When can I use it?**

When can I not use it? Give an example of where I use it. Give an example of where I can’t use it. Why does it work? Give an example.

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**#6: Law of Negative Exponents: A base raised to a**

negative power is the reciprocal of the base to the positive power. So, when I have a negative exponent, I take the reciprocal and change the power to a positive.

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Try these:

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SOLUTIONS

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SOLUTIONS

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**Questions What is the sixth law of exponents? When can I use it?**

When can I not use it? Give an example of where I use it. Give an example of where I can’t use it. Why does it work? Give an example.

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**#7: Zero as an exponent: Anything to the zero power is 1.**

So whenever I raise anything to the zero power it is always 1!

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Try these:

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SOLUTIONS

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**Questions What is the seventh law of exponents? When can I use it?**

When can I not use it? Give an example of where I use it. Give an example of where I can’t use it. Why does it work? Give an example.

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