1. ## Problems to Check

Some more problems I would like checked please. Numbers in red are exponents. My answers are in bold.

Problem 1: (Simplify)

(4a2) (5a)

= 42(a2) * 5(a)

= 4a2 * 5a

= 4 * 5 * a2 * a

= 20a2

________

Problem 2: (Simplify)

(-3xy) (4x2y3)

= -3 (x)(y) * 4 (x2)(y3)

= -3xy * 4x2y3

= -3 * 4 * x * x2 *y * y3

= -12x2y3

__________

Problem 3: (Simplify)

(-3x3y2)(5x5y)

= -3(x3)(y2) * 5(x5)(y)

= -3x3y2 * 5x5y

= -3 * 5 * x3 * x5 * y2 * y

= -15x15y2

__________

Problem 4: (Simplify)

(-3ab2c3)(-5ac)

= -3(a)(b2)(c3) * -5(a)(c)

= -3ab2c3 * -5ac

= -3 * -5 * a * b2 * c3 *c

= 15ab2c3

Thanks!

2. Hello, slykksta!

You're forgetting that: . $x \:=\:x^1$

$1)\;(4a^2)(5a)$
We have: . $(4\cdot a^2)\cdot(5\cdot a) \;=\;(4\cdot5)\cdot(a^2\cdot a^{{\color{red}1}}) \:=\:20\,a^{{\color{red}3}}$

$2) \;(\text{-}3xy) (4x^2y^3)$
We have: . $(\text{-}3\cdot x\cdot y)\cdot(4\cdot x^2\cdot y^3) \;=\;(\text{-}3)(4)\cdot (x^{{\color{red}1}}\cdot x^2)\cdot(y^{{\color{red}1}}\cdot y^3) \;=\;-12\,x^{{\color{red}3}}\,y^{{\color{red}4}}$

$3)\;(\text{-}3x^3y^2)(5x^5y)$
We have: . $(\text{-}3\cdot x^3\cdot y^2)\cdot (5\cdot x^5\cdot y) \;=\;(\text{-}3)(5)\cdot(x^3\cdot x^5)\cdot(y^2\cdot y^{{\color{red}1}}) \;=\;-15\,x^{{\color{red}8}}\,y^{{\color{red}3}}$

$4)\;(\text{-}3ab^2c^3)(\text{-}5ac)$
We have: . $(\text{-}3\cdot a\cdot b^2\cdot c^3)\cdot(\text{-}5\cdot a\cdot c) \;=\;(\text{-}3)(\text{-}5)\cdot(a^{{\color{red}1}}\cdot a^{{\color{red}1}})\cdot (b^2)\cdot(c^3\cdot c^{{\color{red}1}}) \;=\;15\,a^{{\color{red}2}}\,b^2\,c^{{\color{red}4 }}$

3. Originally Posted by slykksta
Some more problems I would like checked please. Numbers in red are exponents. My answers are in bold.

Problem 1: (Simplify)

(4a2) (5a)

= 42(a2) * 5(a)

= 4a2 * 5a

= 4 * 5 * a2 * a

= 20a2

________
Several of your steps here don't make sense.
$(4a^2)(5a) = (4 \cdot 5)(a^2 \cdot a) = 20a^{2 + 1} = 20a^3$

Originally Posted by slykksta
Problem 2: (Simplify)

(-3xy) (4x2y3)

= -3 (x)(y) * 4 (x2)(y3)

= -3xy * 4x2y3

= -3 * 4 * x * x2 *y * y3

= -12x2y3

__________
I'm seeing a pattern here. Recall the rule for addition of exponents:
$a^n \cdot a^m = a^{n + m}$

So $x \cdot x^2 = x^1 \cdot x^2 = x^{1 + 2} = x^3$.

Try this one again.

Originally Posted by slykksta
Problem 3: (Simplify)

(-3x3y2)(5x5y)

= -3(x3)(y2) * 5(x5)(y)

= -3x3y2 * 5x5y

= -3 * 5 * x3 * x5 * y2 * y

= -15x15y2

__________
Ah! I see. You are multiplying the exponents.
$x^3 \cdot x^5 \neq x^{15}$

$x^3 \cdot x^5 = x^{3 + 5} = x^8$

You multiply exponents in this situation:
$(a^n)^m = a^{nm}$

Originally Posted by slykksta
Problem 4: (Simplify)

(-3ab2c3)(-5ac)

= -3(a)(b2)(c3) * -5(a)(c)

= -3ab2c3 * -5ac

= -3 * -5 * a * b2 * c3 *c

= 15ab2c3
Same problems as I mentioned above.

-Dan