Question

e ( x^3 cdot x^4 )
o ( 3x^2 cdot x )
t ( 2x^2 cdot 3x )
i ( x cdot x^2 cdot x^3 )
a ( x^4(-3x^2) )
h ( (-2x^2)(-2x) )
e ( x(-x^4)(-x^4) )

Explanation:

Step1: Apply exponent product rule

For \(x^3 \cdot x^4\), add exponents: \(x^{3+4} = x^7\)

Step2: Apply exponent product rule

For \(3x^2 \cdot x\), add exponents: \(3x^{2+1} = 3x^3\)

Step3: Multiply coefficients, add exponents

For \(2x^2 \cdot 3x\): \(2 \cdot 3 = 6\), \(x^{2+1}=x^3\), result \(6x^3\)

Step4: Add exponents for like bases

For \(x \cdot x^2 \cdot x^3\): \(x^{1+2+3}=x^6\)

Step5: Multiply coefficients, add exponents

For \(x^4(-3x^2)\): \(1 \cdot (-3) = -3\), \(x^{4+2}=x^6\), result \(-3x^6\)

Step6: Multiply coefficients, add exponents

For \((-2x^2)(-2x)\): \((-2) \cdot (-2)=4\), \(x^{2+1}=x^3\), result \(4x^3\)

Step7: Multiply coefficients, add exponents

For \(x(-x^4)(-x^4)\): \(1 \cdot (-1) \cdot (-1)=1\), \(x^{1+4+4}=x^9\), result \(x^9\)

Answer:

E: \(x^7\)
O: \(3x^3\)
T: \(6x^3\)
I: \(x^6\)
A: \(-3x^6\)
H: \(4x^3\)
E: \(x^9\)