The commutative property lets us reorganize the expression.

$\displaystyle 78k*2k=78*k*2*k=78*2*k*k$

By separating the whole numbers and the variables, we can easily multiply.

$\displaystyle 78*2=156$

$\displaystyle k*k=k^2$

$\displaystyle 72*2*k*k=156*k^2=156k^2$

$\displaystyle 78k*2k=156k^{2}$

Answer: $\displaystyle 156k^{2}$

Multiply the whole numbers and add the variables:

$\displaystyle 25m*15m^{2}=375m^{3}$

Answer: $\displaystyle 375m^{3}$

The commutative property lets us reorganize the expression.

$\displaystyle 25m*15m^2=25*m*15*m^2=25*15*m*m^2$

By separating the whole numbers and the variables, we can easily multiply.

$\displaystyle 25*15=375$

$\displaystyle m*m^2=m^3$

$\displaystyle 25*15*m*m^2=375*m^3=375m^3$

$\displaystyle 25m*15m^{2}=375m^{3}$

Answer: $\displaystyle 375m^{3}$

$\displaystyle x(-2-x)=(x)(-2)+(x)(-x)=-2x+(-x^2)=-2x-x^2$

Multiply the numbers and multiply the variables:

$\displaystyle 7n\cdot 3n=21n^{2}$

Answer: $\displaystyle 21n^{2}$

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$\displaystyle (4 * 2) (v^{3}*v*v)(x*x^{3})(y^{2})$ 

When multiplying variables of the same type, you add their exponents together. This gets you:

$\displaystyle (8)(v^{3+1+1})(x^{1+3})(y^2)$

$\displaystyle (8) (v^{5})(x^{4})(y^{2})$

This is the same as:

$\displaystyle 8x^{4}y^{2}v^{5}$

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

 $\displaystyle (10)(e)(f^{4} *f)(t * t^{2})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$\displaystyle (10)(e)(f^{4+1})(t^{1+2})$

$\displaystyle (10)(e)(f^{5})(t^{3})$

This is the same as:

$\displaystyle 10ef^{5}t^{3}$

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$\displaystyle (4 *3)(e*e*e *e*e*e*e) (f*f*f*f**f*f)$

When multiplying variables of the same type, you add their exponents together. (All of these variables have exponents of 1.) This gets you:

$\displaystyle (12)(e^{1+1+1+1+1+1+1})(f^{1+1+1+1+1+1})$

 $\displaystyle (12)(e^{7}) (f^{6})$

This is the same as:

$\displaystyle 12e^{7}f^{6}$

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$\displaystyle (2)(e * e^{2})(f^{6}*f^{2})(u*u^{7})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$\displaystyle (2)(e^{1+2})(f^{6+2})(u^{1+7})$

$\displaystyle (2)(e^{3})(f^{8})(u^{8})$ 

This is the same as:

$\displaystyle 2e^{3}f^{8}u^{8}$

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

 $\displaystyle (2*4)(g*g^{2})(r^{2}*r^{3})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$\displaystyle (8)(g^{1+2})(r^{2+3})$

 $\displaystyle (8)(g^{3})(r^{5})$

This is the same as:

$\displaystyle 8g^{3}r^{5}$