Question

Use your results in part(a) to explain how to find$(\mathrm{a}\times {10}^{\mathrm{n}})\times (\mathrm{b}\times {10}^{\mathrm{m}})$ and $(\mathrm{a}\times {10}^{\mathrm{n}})÷(\mathrm{b}÷{10}^{\mathrm{m}}).$ Describe any properties that you use.

Answer 1

Step1 . To find $(\mathrm{a}\times {10}^{\mathrm{n}})\times (\mathrm{b}\times {10}^{\mathrm{m}})$ , we need multiply a and b first and then multiply powers .

$(\mathrm{a}\times {10}^{\mathrm{n}})\times (\mathrm{b}\times {10}^{\mathrm{m}})$ $=(\mathrm{a}\times \mathrm{b})\times ({10}^{\mathrm{n}}\times {10}^{\mathrm{m}})=(\mathrm{a}\times \mathrm{b})\times \left({10}^{\mathrm{n}+\mathrm{m}}\right)$

Exponent Law that is used is ${\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}}$

Step 2. To find$(\mathrm{a}\times {10}^{\mathrm{n}})÷(\mathrm{b}\times {10}^{\mathrm{m}})$ , we need divide a and b first and then divid powers .

$(\mathrm{a}\times {10}^{\mathrm{n}})÷(\mathrm{b}\times {10}^{\mathrm{m}})$ $=(\mathrm{a}÷\mathrm{b})\times ({10}^{\mathrm{n}}÷{10}^{\mathrm{m}})=(\mathrm{a}÷\mathrm{b})\times \left({10}^{\mathrm{n}-\mathrm{m}}\right)$

Exponent Law that is used is ${\mathrm{a}}^{\mathrm{m}}÷{\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}$