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- Base
- Yeah of course bro. An exponent has a base. A base can be a whole number, a fraction, or a variable.
- Yes!!
- Are 4 and x bases?
- Hey. I need some help. I got a test on exponent rules this week and I don't know anything about it. What is an exponent?
- Exponent
- So the number on the upper right of the base is called an exponent. It represents the power to which the base is to be raised.
- You are so right! You're getting the hang of this quickly!
- So in the example 4^3, is 4 the base and 3 the exponent?
- Product Rule/Quotient Rule
- Now there are two rules called the product rule and quotient rule. The product rule is when you add the exponents when you are multiplying two of the same variables. For the quotient rule, you subtract the exponents when you are dividing by two of the same variables.
- For sure, in this problem x^2 times x^2, you keep the x by itself and add the exponents to get 4. The answer is x^4. For x^4/x^2, you would subtract 4 and 2 to get x^2.
- Oh that makes sense.
- I am still a little confused. Could you give me an example?
- Power to Power Rule
- Great question! The power to power rule is a rule where you multiply two powers that are raised and the base remains the same. So if you had (x^2)^2, you multiply 2 and 2 to get x^4.
- What is the power to power rule?
- Zero Exponent Rule
- Yeah, that's the zero exponent rule. But, when you have zero as the base, the answer would be undefined instead of 1.
- Yeah!! You rock!
- So 10^0 is equal to 1, but 0^0 is undefined.
- There's also this rule where the exponent is 0 and the answer will equal to 1?
- Negative Exponent Rule
- A rule you must understand is the negative exponent rule. The negative exponent rule is x^-n = 1/x^n. And this is because negative exponents are reciprocal of the original number.
- Yes!
- I understand what you are saying, so 2^-3 = 1/2^3.
- convert from radical notation to exponentnotation/convert exponent notation to radical notation
- Now, to convert radical notation into exponential notation, the equation is a = a^1/n. The index of the radical exponent is always the denominator and the radicand of the exponent is always the base of the exponential notation.
- You got it! And to convert exponent notation to radical notation, the base stays the same, and the numerator becomes the exponent. The denominator becomes the root of the radical.
- I get it now!
- So 3√5 is 5^1/3 in exponential notation.
- Rule for when bases are different butexponents are the same - multiplication/division
- Correct! It also works for division as well. So in the case the problem is 3^2/5^2 = (3/5)^2.
- The formula is a^m*b^m = (ab)^m. For example 3^2 * 5^2 = (5 *3)^2.
- Ahh. So you multiplied the bases first then applied the exponent.
- Oh and can you remind me of the formula for dividing or multiplying numbers with different bases but similar exponents.
- Final Project!
- You did great! I think you are ready for your exponent rules test!
- Yay!! I learned the exponent rules!
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