Question

Which of the following properties are used to when rewriting the expression (3/×^3)^-2 ?

a) Power rule and reciprocal rule
b) Product rule and quotient rule
c) Exponent rule and distributive property
d) Associative property and identity property

Answer 1

The proper rules for rewriting the expression (3/x³)⁻² are the power rule and the reciprocal rule. The power rule multiplies exponents when raising an exponent to another power, while the reciprocal rule converts a negative exponent into a reciprocal expression.

Step-by-step explanation:

The expression (3/x³)⁻² involves working with the rules for dealing with exponents. Particularly, we are looking at the power rule for exponents and the rule for negative exponents, also known as the reciprocal rule.

Using the power rule, when we raise an exponent to another power, we multiply the exponents. For example, (x^n)^m = x^(n*m). In our case, we would apply this as (3/x³)⁻² = x⁶.

Then using the reciprocal rule, we know that x⁻ⁿ = 1/xⁿ. So taking the reciprocal of our base 3, which is already raised to a negative exponent, the expression would become (1/3)² / x⁶, which simplifies to 1/9x⁶.

Therefore, the correct answer to the question is a) Power rule and reciprocal rule.