13. The expression $\frac{2 a^{6} b^{2} c}{10 a^{2} b^{-2} c}$ written in simplest form is
a. $\quad 5 a^{4} b^{4}$
b. $\quad \frac{a^{4}}{5}$
c. $\frac{a^{4} b^{4}}{5}$
d. $\quad 5 a^{8} b^{0} c^{2}$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\boxed{\frac{a^{4} b^{4}}{5}}$

Steps

Step 1 ：Simplify the expression: $\frac{2 a^{6} b^{2} c}{10 a^{2} b^{-2} c}$

Step 2 ：Combine like terms: $\frac{2 a^{6-2} b^{2-(-2)}}{10}$

Step 3 ：Simplify the exponents: $\frac{2 a^{4} b^{4}}{10}$

Step 4 ：Divide the coefficients: $\frac{a^{4} b^{4}}{5}$

Step 5 ：Final Answer: $\boxed{\frac{a^{4} b^{4}}{5}}$