Question

3 multiple choice 1 point
to simplify $(x^{3}x^{4})^{2}$ we must use the...
both product and power rule
both quotient and product rule
power of powers rule
product of powers rule
quotient of powers rule

Explanation:

Step1: Analyze inner expression

First, simplify $x^3x^4$ using the Product of Powers Rule: $x^a \cdot x^b = x^{a+b}$.
Expression: $x^3x^4 = x^{3+4} = x^7$

Step2: Apply outer exponent

Next, simplify $(x^7)^2$ using the Power of Powers Rule: $(x^a)^b = x^{a \cdot b}$.
Expression: $(x^7)^2 = x^{7 \cdot 2} = x^{14}$

Step3: Identify used rules

Both the Product of Powers Rule and Power of Powers Rule (combined as Power Rule for exponents) were used.

Answer:

Both Product and Power Rule