Question

Which rules of exponents will be used to evaluate this expression? Check all that apply.

a) Product of powers
b) Quotient of powers
c) Power of a power
d) Power of a product

Answer 1

The rules of exponents used to evaluate expressions include the product of powers, quotient of powers, power of a power, and power of a product, depending on the specifics of the expression.

Step-by-step explanation:

When evaluating expressions with exponents, there are several rules that may apply, depending on the structure of the expression:

• Product of Powers: Used when multiplying two exponentiated terms with the same base, where you add the exponents (A × 10b) × (C × 10d) = AC × 10b+d.
• Quotient of Powers: Used when dividing two powers with the same base, where you subtract the exponents of the denominator's base from the numerator's base (A × 10b) ÷ (C × 10d) = (A/C) × 10b-d.
• Power of a Power: Used when an exponentiated term is raised to an additional power, where you multiply the exponents (5x)y = 5xy.
• Power of a Product: Used when a product of terms is raised to a power, where you apply the exponent to each term within the parentheses ((A × B)n = An × Bn).

If we consider the multiplication and cubing of exponentials, you multiply digit terms normally, add exponents when dealing with products of powers, and multiply the exponents by the power when it's a power of a power.