Question

How can you write general rules involving properties of exponents?

Answer 1

To write general rules involving properties of exponents, follow these rules: multiply exponents when raising a power to another power, add exponents when multiplying two exponentiated quantities with the same base, and subtract exponents when dividing two exponentiated quantities with the same base.

Step-by-step explanation:

When dealing with exponents, there are several general rules to keep in mind:

1. When raising a power to another power, multiply the exponents. For example, (2^3)^2 is equal to 2^(3*2) = 2^6.
2. When multiplying two exponentiated quantities with the same base, add the exponents. For example, (3^2) * (3^4) is equal to 3^(2+4) = 3^6.
3. When dividing two exponentiated quantities with the same base, subtract the exponents. For example, (4^5) / (4^2) is equal to 4^(5-2) = 4^3.

Answer 2

1.- b^m b^n = b^(n+m)
In the product with equal bases the exponents are added.
2 .- (b ^ m) ^ n = b ^ (n m)
A base with double exponent; the exponents multiply.
3 .- (ab) ^ n = a ^ n * b ^ n
A product raised to an exponent; each factor is raised to that exponent.
4 .- (b ^ n) / (b ^ m) = b ^ (n-m)
In the quotient with equal bases the exponents are subtracted
5.- (a / b) ^ n = (a ^ n) / (b ^ n)
A ratio raised to an exponent; each term is raised to that exponent.
6.- (a / b) ^ - n = (b / a) ^ n
A quotient with a negative exponent is the reciprocal of the positive quotient