# How do you simplify (20b^10) /( 10b^20)?

May 27, 2018

$2 {b}^{-} 10$

#### Explanation:

You can split the fraction into two:
$\frac{20}{10}$ and ${b}^{10} / {b}^{20}$ And you can work out each separate.

$\frac{20}{10} = 2$

Using the formula
${a}^{b} / {a}^{c} = {a}^{b - c}$ you can work out the second fraction.

${b}^{10} / {b}^{20} = {b}^{10 - 20} = {b}^{-} 10$

Then you can multiply $2$ by ${b}^{-} 10$ to get $2 {b}^{-} 10$

May 27, 2018

$\frac{2}{b} ^ 10$

#### Explanation:

$\frac{20 {b}^{10}}{10 {b}^{20}}$

$\frac{2 \times 10 \times {b}^{10}}{1 \times 10 \times {b}^{20}}$

$\frac{2 \times \cancel{10} \times {b}^{10}}{1 \times \cancel{10} \times {b}^{20}}$

$\frac{2 \times 1 \times {b}^{10}}{1 \times 1 \times {b}^{20}}$

$\frac{2 {b}^{10}}{b} ^ 20$

$2 {b}^{10} \div {b}^{20}$

Recall;

${x}^{a} \div {x}^{b} = {x}^{a - b}$

Hence;

$2 {b}^{10} \div {b}^{20} = 2 {b}^{10 - 20}$

$2 {b}^{-} 10$

But: ${x}^{-} 1 = \frac{1}{x}$

Therefore;

$\frac{2}{b} ^ 10$

May 27, 2018

$2 {b}^{-} 10$

#### Explanation:

$\frac{20 {b}^{10}}{10 {b}^{20}}$

It might be helpful to rewrite this as two separate fractions.

$\frac{20}{10} \cdot {b}^{10} / {b}^{20}$

$2 \cdot {b}^{10} / {b}^{20}$

We can simplify the second fraction if we remember a little rule: ${n}^{a} / {n}^{b} = {n}^{a - b}$. In other words, ${b}^{10} / {b}^{20}$ will equal ${b}^{10 - 20}$ or ${b}^{-} 10$.

$2 \cdot {b}^{-} 10$

$2 {b}^{-} 10$