Question

1. $x^3 * x^4$

answer:

1. $2(3x^3)(x^5)$

answer:

1. $2(3x^{34})(-x^{25})$

answer:

1. $(3x^3y^2)(-x^5y)$

answer:
simplify the exponents

Explanation:

Step1: Apply exponent product rule

For $x^3 * x^4$, use $x^a * x^b = x^{a+b}$:
$x^{3+4} = x^7$

Step2: Multiply constants, add exponents

For $2(3x^3)(x^5)$:
First multiply constants: $2*3=6$
Then add exponents of $x$: $x^{3+5}=x^8$
Combine: $6x^8$

Step3: Multiply constants, add exponents

For $2(3x^{34})(-x^{25})$:
First multiply constants: $2*3*(-1)=-6$
Then add exponents of $x$: $x^{34+25}=x^{59}$
Combine: $-6x^{59}$

Step4: Multiply constants, add exponents

For $(3x^3y^2)(-x^5y)$:
First multiply constants: $3*(-1)=-3$
Add exponents of $x$: $x^{3+5}=x^8$
Add exponents of $y$: $y^{2+1}=y^3$
Combine: $-3x^8y^3$

Answer:

1. $x^7$
2. $6x^8$
3. $-6x^{59}$
4. $-3x^8y^3$