To simplify the given expression [tex]\(\frac{4a^2(a^3)}{16b(b^2)}\)[/tex], let's proceed step-by-step:
1. Expand the numerator and the denominator:
The numerator is:
[tex]\[
4a^2(a^3) = 4a^{2+3} = 4a^5
\][/tex]
The denominator is:
[tex]\[
16b(b^2) = 16b^{1+2} = 16b^3
\][/tex]
So, the expression now becomes:
[tex]\[
\frac{4a^5}{16b^3}
\][/tex]
2. Simplify the constants:
Divide both the numerator and the denominator by the common factor 4:
[tex]\[
\frac{4a^5}{16b^3} = \frac{4 \div 4 \cdot a^5}{16 \div 4 \cdot b^3} = \frac{a^5}{4b^3}
\][/tex]
Thus, the simplified expression is:
[tex]\[
\frac{a^5}{4b^3}
\][/tex]
To summarize:
- We expanded the powers in the numerator and the denominator.
- We combined the like terms.
- We simplified by dividing the numerator and the denominator by the greatest common factor, which is 4.
So the correct simplified form of the given expression is:
[tex]\[
\frac{a^5}{4b^3}
\][/tex]
