Let's simplify the given expression step by step:
[tex]\[
\frac{18 m^{10} n^{-2} p^6}{30 m^{-6} n^{16} p^3}
\][/tex]
### Step 1: Simplify the Coefficients
First, divide the coefficients [tex]\(18\)[/tex] and [tex]\(30\)[/tex]:
[tex]\[
\frac{18}{30} = 0.6
\][/tex]
### Step 2: Simplify the Powers of [tex]\(m\)[/tex]
Next, simplify the exponents of [tex]\(m\)[/tex] using the properties of exponents (specifically, [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]):
[tex]\[
m^{10} \div m^{-6} = m^{10 - (-6)} = m^{10 + 6} = m^{16}
\][/tex]
### Step 3: Simplify the Powers of [tex]\(n\)[/tex]
Now, simplify the exponents of [tex]\(n\)[/tex]:
[tex]\[
n^{-2} \div n^{16} = n^{-2 - 16} = n^{-18}
\][/tex]
### Step 4: Simplify the Powers of [tex]\(p\)[/tex]
Finally, simplify the exponents of [tex]\(p\)[/tex]:
[tex]\[
p^6 \div p^3 = p^{6 - 3} = p^3
\][/tex]
### Step 5: Combine Everything
Combining all the simplified parts together, we get:
[tex]\[
0.6 m^{16} n^{-18} p^3
\][/tex]
So, the simplified form of the expression is:
[tex]\[
\boxed{0.6 m^{16} n^{-18} p^3}
\][/tex]
