Question

Simplify 81p6q2÷3p2q5 HELPPP​

Answer 1

`\displaystyle (81\, p^(6)\, q^(2))/(3\, p^(2) \, q^(5)) = (27\, p^(4))/(q^(3))`.

Explanation:

Make use of the fact that for any
`x \\e 0` and integer
`n`:

`\displaystyle (1)/(x^(n)) = x^(-n)`.

For example, in this question:

`\displaystyle (1)/(p^(2)) = p^(-2)`.

`\displaystyle (1)/(q^(5)) = q^(-5)`.

Thus, the original expression would be equivalent to:

`\begin{aligned}& (81\, p^(6)\, q^(2))/(3\, p^(2) \, q^(5)) \\ =\; & (81)/(3)\, (p^(6)\, p^(-2))\, (q^(2)\, q^(-5)) \\ =\; & 27\, (p^(6)\, p^(-2))\, (q^(2)\, q^(-5))\end{aligned}`.

Also make use of the fact that for any
`x \\e 0`, integer
`m`, and integer
`n`:

`x^(m)\, x^(n) = x^(m + n)`.

Thus:

`\begin{aligned}& 27\, (p^(6)\, p^(-2))\, (q^(2)\, q^(-5)) \\=\; & 27\, p^(6 + (-2))\, q^(2 + (-5)) \\ =\; & 27\, p^(4)\, q^(-3) \\ =\; & (27\, p^(4))/(q^(3))\end{aligned}`.