How do you simplify (b^8c^6d^5)(8b^6c^2d)?

Dec 24, 2016

$8 {b}^{14} {c}^{8} {d}^{6}$

Explanation:

for mulıplication only sum the power of the same terms, i.e:
${b}^{8} \cdot {b}^{6} = {b}^{14}$ then similarly ${c}^{6} \cdot {c}^{2} = {c}^{8}$ and ${d}^{5} \cdot d = {d}^{6}$

Therefore $\left({b}^{8} {c}^{6} {d}^{5}\right) \left(8 {b}^{6} {c}^{2} d\right) = 8 {b}^{14} {c}^{8} {d}^{6}$

Dec 24, 2016

$8 {b}^{14} {c}^{8} {d}^{6}$

Explanation:

Step 1) Combine the terms in parenthesis:

$\left(\textcolor{red}{{b}^{8}} \textcolor{b l u e}{{c}^{6}} \textcolor{g r e e n}{{d}^{5}}\right) \left(8 \textcolor{red}{{b}^{6}} \textcolor{b l u e}{{c}^{2}} \textcolor{g r e e n}{d}\right) \to \textcolor{red}{{b}^{8}} \textcolor{b l u e}{{c}^{6}} \textcolor{g r e e n}{{d}^{5}} 8 \textcolor{red}{{b}^{6}} \textcolor{b l u e}{{c}^{2}} \textcolor{g r e e n}{d}$

Now we can group like terms:

$\textcolor{red}{{b}^{8}} \textcolor{b l u e}{{c}^{6}} \textcolor{g r e e n}{{d}^{5}} 8 \textcolor{red}{{b}^{6}} \textcolor{b l u e}{{c}^{2}} \textcolor{g r e e n}{d} \to 8 \textcolor{red}{{b}^{8}} \textcolor{red}{{b}^{6}} \textcolor{b l u e}{{c}^{6}} \textcolor{b l u e}{{c}^{2}} \textcolor{g r e e n}{{d}^{5}} \textcolor{g r e e n}{d}$

For the next step in the simplification we need to use the following rule for exponents:

$\textcolor{p u r p \le}{{x}^{a} {x}^{b} = {x}^{a + b}}$

Using this rule we can now combine like terms:

$8 \textcolor{red}{{b}^{8}} \textcolor{red}{{b}^{6}} \textcolor{b l u e}{{c}^{6}} \textcolor{b l u e}{{c}^{2}} \textcolor{g r e e n}{{d}^{5}} \textcolor{g r e e n}{d} \to 8 \textcolor{red}{{b}^{8 + 6}} \textcolor{b l u e}{{c}^{6 + 2}} \textcolor{g r e e n}{{d}^{5 + 1}} \to 8 \textcolor{red}{{b}^{14}} \textcolor{b l u e}{{c}^{8}} \textcolor{g r e e n}{{d}^{6}}$