Operations with monomials

Calculate the product of the following monomials. Remember to multiply the coefficients together and add the exponents of identical letters:

1. a) $(3x^{2}) \cdot (5x^{4})$
2. b) $(-2a^{3}) \cdot (4a)$
3. c) $(\frac{1}{2}x) \cdot (6x^{2})$
4. d) $(-x^{2}) \cdot (-x^{3})$

Perform the following divisions of monomials. Remember to divide the coefficients and subtract the exponents of the letters:

1. a) $(12x^{5}) : (3x^{2})$
2. b) $(-10a^{4}) : (5a^{3})$
3. c) $(15x^{3}y^{2}) : (3x^{2}y)$
4. d) $(4x^{2}) : (2x^{2})$

Calculate the power of these monomials. Do not forget to raise both the coefficient and the literal part to the indicated exponent:

1. a) $(2x^{3})^{2}$
2. b) $(-3a^{2})^{2}$
3. c) $(x^{4})^{3}$
4. d) $(-2x)^{3}$

Simplify the following expressions by adding and subtracting like monomials:

1. a) $5a + 3a - 2a$
2. b) $4x^{2} - x^{2} + 7x^{2}$
3. c) $3ab - 5ab + ab$
4. d) $x + x + x + x$

Find the algebraic expression representing the perimeter of the following rectangular plot for a school garden. Once you have the expression, fully simplify it by combining like terms.

In a racing video game, for each gold coin collected you get $5x$ points and for each silver coin you get $2x$ points.

If in a game a player has collected 4 gold coins and 6 silver coins:

1. a) Write the monomial representing the total points from the gold coins.
2. b) Write the monomial representing the total points from the silver coins.
3. c) Add both monomials to find the total points for the game.

You can do it on paper and send a photo with your answer.