8. simplify: $(3a^{3}b^{5}c)^{2}(4ab^{2}c^{3})(2ab^{-5})^{0}$

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Accepted Answer

# Explanation:
## Step1: Simplify the power of a product
First, we simplify $(3a^{3}b^{5}c)^{2}$ using the power of a product rule $(xy)^n = x^n y^n$.
$$
\begin{align*}
(3a^{3}b^{5}c)^{2}&=3^{2}(a^{3})^{2}(b^{5})^{2}c^{2}\
&=9a^{6}b^{10}c^{2}
\end{align*}
$$
## Step2: Simplify the zero exponent
Next, we simplify $(2ab^{-5})^{0}$. Any non - zero number to the power of 0 is 1, so $(2ab^{-5})^{0}=1$ (assuming $2ab^{-5}
eq0$, which is true for non - zero $a$ and $b$).
## Step3: Multiply the remaining terms
Now we multiply $9a^{6}b^{10}c^{2}$, $4ab^{2}c^{3}$ and 1. Using the product rule of exponents $x^m\times x^n=x^{m + n}$ for the same base:
$$
\begin{align*}
&9a^{6}b^{10}c^{2}\times4ab^{2}c^{3}\times1\
=&(9\times4)\times(a^{6}\times a)\times(b^{10}\times b^{2})\times(c^{2}\times c^{3})\
=&36\times a^{6 + 1}\times b^{10+2}\times c^{2 + 3}\
=&36a^{7}b^{12}c^{5}
\end{align*}
$$

# Answer:
$36a^{7}b^{12}c^{5}$

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QUESTION IMAGE

Question

Explanation:

Step1: Simplify the power of a product

Step2: Simplify the zero exponent

Step3: Multiply the remaining terms

Answer: