The 8 Exponent Rules
By: Connor Holley, 1st Period
INDEX
Quotient of Powers
Zero Exponent
Product of Powers
Power of a Power
Negative exponent
Power of a Quotient
One Exponent
Power of a product
Product of Powers
Product of powers is relatively simple. When you multiply two numbers with the same base, you can add the exponents. For example, 4^4 * 4^2. Now, we add the exponents, and keep the base to get 4^6. Makes sense, doesn't it?
Rule 2
Quotient of Powers
The quotient of powers rule may sound confusing, but it really isn't. When you divide two numbers with the same base, you keep the base and SUBTRACT the exponents, and the base CANNOT equal 0. For example, 4^3/4^2. We subtract the exponents to get 4^1 or 4.
Zero exponent rule
The zero exponent rule comes into play when you see a number with the exponent of 0. This automatically means the base will equal 1. For example, 8^0=1 I hope you enderstand the zero exponent rule
Negative exponent rule. For any number raised to a negative exponent, place the power as a denominator to make it a positive exponent. For example, I have 5^-4. You cant solve with a negative exponent, so I would put it as the denominator and one as the numerator to get 1/5^4
Power of a power
When you raise a power to a power, you multiply the exponents. it should look like this :(x^y)^f=x^yf. Now, let's try a real example: (4^2)^2. now, we multiply the exponents to get 4^4 and then solve for 64.
Power of a quotient rule
For any numbers where a(numerator) and b(denominator) are raised to another power, raise both the numerator and denominator to the new power. for example, (4/5)^2. We raise both up to get 4^2/5^2, which equals 8/25. I hope you understand the power of a quotient rule.
Power of a product
The power of a product rule is when you find the power of each factor in the parenthesis and then multiply it by the exponent outside. For example (4^2*4^3)^2. First , we find the power of each factor and multiply it by 2. this would give us 4^4*4^6. Now we will use the power of a power rule to get 4^10.
One exponent rule
The one exponent rule is the rule where anything to the power of 1 is one. For example, 8^1= 8 or 5^1=5 This is the one exponent rule.
THANKS!
Thanks for watching!
I hope you now understand the 8 exponent rules!
Connor Holley 8 Exponent Rules
Connor Holley
Created on March 18, 2023
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Transcript
The 8 Exponent Rules
By: Connor Holley, 1st Period
INDEX
Quotient of Powers
Zero Exponent
Product of Powers
Power of a Power
Negative exponent
Power of a Quotient
One Exponent
Power of a product
Product of Powers
Product of powers is relatively simple. When you multiply two numbers with the same base, you can add the exponents. For example, 4^4 * 4^2. Now, we add the exponents, and keep the base to get 4^6. Makes sense, doesn't it?
Rule 2
Quotient of Powers
The quotient of powers rule may sound confusing, but it really isn't. When you divide two numbers with the same base, you keep the base and SUBTRACT the exponents, and the base CANNOT equal 0. For example, 4^3/4^2. We subtract the exponents to get 4^1 or 4.
Zero exponent rule
The zero exponent rule comes into play when you see a number with the exponent of 0. This automatically means the base will equal 1. For example, 8^0=1 I hope you enderstand the zero exponent rule
Negative exponent rule. For any number raised to a negative exponent, place the power as a denominator to make it a positive exponent. For example, I have 5^-4. You cant solve with a negative exponent, so I would put it as the denominator and one as the numerator to get 1/5^4
Power of a power
When you raise a power to a power, you multiply the exponents. it should look like this :(x^y)^f=x^yf. Now, let's try a real example: (4^2)^2. now, we multiply the exponents to get 4^4 and then solve for 64.
Power of a quotient rule
For any numbers where a(numerator) and b(denominator) are raised to another power, raise both the numerator and denominator to the new power. for example, (4/5)^2. We raise both up to get 4^2/5^2, which equals 8/25. I hope you understand the power of a quotient rule.
Power of a product
The power of a product rule is when you find the power of each factor in the parenthesis and then multiply it by the exponent outside. For example (4^2*4^3)^2. First , we find the power of each factor and multiply it by 2. this would give us 4^4*4^6. Now we will use the power of a power rule to get 4^10.
One exponent rule
The one exponent rule is the rule where anything to the power of 1 is one. For example, 8^1= 8 or 5^1=5 This is the one exponent rule.
THANKS!
Thanks for watching!
I hope you now understand the 8 exponent rules!