Question

(x^3)^4 = x?
only fill in the power for the answer
expand this out to help

question 4
1 pts
simplify
x^3(x^4 + x^2) =

x^12 + x^6

x^7 + x^5

x^12

x^18

Explanation:

First Problem: \((x^3)^4 = x^?\)

Step1: Recall exponent rule

When raising a power to a power, we multiply the exponents. The formula is \((a^m)^n=a^{m\times n}\). Here, \(a = x\), \(m = 3\), and \(n=4\).

Step2: Calculate the exponent

Multiply the exponents: \(3\times4 = 12\). So \((x^3)^4=x^{12}\).

Step1: Apply distributive property

The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = x^3\), \(b=x^4\), and \(c = x^2\). So we have \(x^3\times x^4+x^3\times x^2\).

Step2: Apply exponent rule for multiplication

When multiplying exponents with the same base, we add the exponents. The formula is \(a^m\times a^n=a^{m + n}\). For \(x^3\times x^4\), \(m = 3\), \(n = 4\), so \(x^{3+4}=x^7\). For \(x^3\times x^2\), \(m = 3\), \(n=2\), so \(x^{3 + 2}=x^5\). Combining these, we get \(x^7+x^5\).

Answer:

12

Question 4: Simplify \(x^3(x^4 + x^2)\)