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power rules exponents quick check
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GPT 3.5
The power rules for exponents are as follows:
1. Product Rule: When multiplying two powers with the same base, add the exponents: a^m * a^n = a^(m + n)
Example: 2^3 * 2^4 = 2^(3 + 4) = 2^7 = 128
2. Quotient Rule: When dividing two powers with the same base, subtract the exponents: a^m / a^n = a^(m - n)
Example: 5^6 / 5^2 = 5^(6 - 2) = 5^4 = 625
3. Power Rule: When raising a power to another power, multiply the exponents: (a^m)^n = a^(m * n)
Example: (3^2)^4 = 3^(2 * 4) = 3^8 = 6,561
4. Zero Rule: Any number raised to the power of zero is equal to 1: a^0 = 1
Example: 7^0 = 1
5. Negative Exponent Rule: A negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent: a^(-n) = 1 / a^n
Example: 2^(-3) = 1 / 2^3 = 1 / 8 = 0.125
1. Product Rule: When multiplying two powers with the same base, add the exponents: a^m * a^n = a^(m + n)
Example: 2^3 * 2^4 = 2^(3 + 4) = 2^7 = 128
2. Quotient Rule: When dividing two powers with the same base, subtract the exponents: a^m / a^n = a^(m - n)
Example: 5^6 / 5^2 = 5^(6 - 2) = 5^4 = 625
3. Power Rule: When raising a power to another power, multiply the exponents: (a^m)^n = a^(m * n)
Example: (3^2)^4 = 3^(2 * 4) = 3^8 = 6,561
4. Zero Rule: Any number raised to the power of zero is equal to 1: a^0 = 1
Example: 7^0 = 1
5. Negative Exponent Rule: A negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent: a^(-n) = 1 / a^n
Example: 2^(-3) = 1 / 2^3 = 1 / 8 = 0.125