Question

Simplify the following.

a) 3x³y x 2x³y
b) xz² x 4x¹z³
c) 4a³b² x 3a b³
d) 6s't x st

Answer 1

Alright so in order to simplify the following ,we firstly must know that when the base of the exponents are same then their power gets added while performing multiplication.

Thus,

for a) 3x^2y^4*2x^6y

• 3*2(x^(2+6))(y^(4+1)) = 6x^8y^5

for b) xz^3*4x^4z^5

• 4(x^(1+4))(z^(3+5)) = 4x^5z^8

for c) 4a^3b^2*3a^6b^5

• 4*3(a^(3+6))(b^(2+5)) = 12a^9b^7

for d) 6s^5t*s^4t^2

• 6(s^(5+4))(t^(1+2)) = 6s^9t^3

Answer 2

`\textsf{a)}\quad 6x^8y^5`

`\textsf{b)}\quad 4x^5z^8`

`\textsf{c)}\quad 12a^9b^7`

`\textsf{d)}\quad 6s^9t^3`

Explanation:

To simplify the given expressions:

• Express any variables without an exponent as raised to the power of one.
• Multiply any integers.
• Collect terms with the same variable.
• Apply the product rule of exponents.

`\boxed{\begin{array}{rl}\underline{\sf Exponent\;Rules}\\\\\sf Power\;of\;one:&a=a^1\\\\\sf Product:&a^m * a^n=a^(m+n)\\\\\end{array}}`

Question a)

`\large\begin{aligned}3x^2y^4 * 2x^6y&=3x^2y^4 * 2x^6y^1\\\\&=6 x^2x^6 y^4 y^1\\\\&=6 x^(2+6) \:y^(4+1)\\\\&=6 x^(8) y^(5)\end{aligned}`

Question b)

`\large\begin{aligned}xz^3 * 4x^4z^5&=x^1z^3 * 4x^4z^5\\\\&=4 x^1 x^4 z^3 z^5\\\\&=4 x^(1+4)\: z^(3+5)\\\\&=4x^(5)z^(8)\end{aligned}`

Question c)

`\large\begin{aligned}4a^3b^2 * 3a^6b^5&=12a^3a^6b^2b^5\\\\&=12a^(3+6)\:b^(2+5)\\\\&=12a^(9)b^(7)\end{aligned}`

Question d)

`\large\begin{aligned}\s6s^5t * s^4t^2&=6s^5t^1 * s^4t^2\\\\&=6s^5s^4t^1 t^2\\\\&=6s^(5+4)\:t^(1+2)\\\\&=6s^(9)t^(3)\end{aligned}`