Sure! Let's go through the steps to simplify the expression [tex]\(\frac{10 h^3}{25 h^9}\)[/tex].
### Step 1: Simplify the Coefficient
The expression has two main parts: the coefficient (numerical part) and the variable part involving [tex]\( h \)[/tex].
First, let's deal with the coefficient:
[tex]\[
\frac{10}{25}
\][/tex]
To simplify this, we divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 10 and 25 is 5:
[tex]\[
\frac{10 \div 5}{25 \div 5} = \frac{2}{5}
\][/tex]
So, the simplified coefficient is [tex]\(\frac{2}{5}\)[/tex].
### Step 2: Simplify the Variable Part
Next, we handle the variable part. The original variable part of the expression is:
[tex]\[
\frac{h^3}{h^9}
\][/tex]
When you divide powers with the same base, you subtract the exponents:
[tex]\[
h^{3-9} = h^{-6}
\][/tex]
So, the simplified variable part is [tex]\(h^{-6}\)[/tex].
### Step 3: Combine Results
Now, we combine the simplified coefficient with the simplified variable part. The final expression is:
[tex]\[
\frac{2}{5} \cdot h^{-6}
\][/tex]
### Result
Thus, the simplified form of the expression [tex]\(\frac{10 h^3}{25 h^9}\)[/tex] is:
[tex]\[
\frac{2}{5} h^{-6}
\][/tex]
Or equivalently, you can represent the coefficient as a decimal, which gives:
[tex]\[
0.4 h^{-6}
\][/tex]
So, the final simplified expression is:
[tex]\[
0.4 h^{-6}
\][/tex]
