Define- What Two operations can you apply Exponent Rules?
Define- How are exponent rules different from operation rules with numbers?
Define- Copy a picture of all the exponent rules here:
Two operations that can be applied to exponent rules are multiplication and division.
Exponent rules are different from operation rules with numbers because they specifically apply to exponents. Operation rules with numbers, such as addition, subtraction, multiplication, and division, are more general and apply to all numbers.
Unfortunately, as an AI language model, I'm not able to directly copy and paste images here. However, I can describe the exponent rules for you:
1. Product Rule: When multiplying two terms with the same base, you add their exponents.
Example: a^m * a^n = a^(m + n).
2. Quotient Rule: When dividing two terms with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
Example: a^m / a^n = a^(m - n).
3. Power Rule: When raising a power to another power, you multiply the exponents.
Example: (a^m)^n = a^(m × n).
4. Zero Rule: Any nonzero number raised to the power of zero equals 1.
Example: a^0 = 1 (where 'a' is nonzero).
5. Negative Exponent Rule: A number raised to a negative exponent is the reciprocal of the same number raised to the positive exponent.
Example: a^(-n) = 1 / a^n.
6. Product of Powers Rule: When raising a product of terms to an exponent, you can distribute the exponent to each term.
Example: (a * b)^n = a^n * b^n.
7. Quotient of Powers Rule: When raising a quotient of terms to an exponent, you can distribute the exponent to the numerator and denominator separately.
Example: (a / b)^n = a^n / b^n.
8. Power of a Product Rule: When raising a power to a product of terms, you can distribute the exponent to each term.
Example: (a * b)^n = a^n * b^n.
9. Power of a Quotient Rule: When raising a power to a quotient of terms, you can distribute the exponent to the numerator and denominator separately.
Example: (a / b)^n = a^n / b^n.
These rules help simplify expressions involving exponents and make computations easier.