# How do you simplify (0.93^6)(0.93^-8)?

Jun 3, 2018

$= \frac{1}{0.8649} \approx 1.1562$

#### Explanation:

Since these have the same base:

$\left({0.93}^{6}\right) \left({0.93}^{-} 8\right)$

we can use the rule for exponents:

${a}^{n} \cdot {a}^{m} = {a}^{n + m}$

$\left({0.93}^{6}\right) \left({0.93}^{-} 8\right) = {0.93}^{-} 2$

$= \frac{1}{0.93} ^ 2$

$= \frac{1}{0.8649} \approx 1.1562$

Jun 3, 2018

See a solution process below:

#### Explanation:

We can use this rule for exponents to begin the simplification process for the expression:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\left({0.93}^{\textcolor{red}{6}}\right) \left({0.93}^{\textcolor{b l u e}{- 8}}\right) \implies {0.93}^{\textcolor{red}{6} + \textcolor{b l u e}{- 8}} \implies {0.93}^{\textcolor{red}{6} - \textcolor{b l u e}{8}} \implies {0.93}^{-} 2$

Next, we can use this rule for exponents to eliminate the negative exponent:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${0.93}^{\textcolor{red}{- 2}} \implies \frac{1}{0.93} ^ \textcolor{red}{- - 2} \implies \frac{1}{0.93} ^ \textcolor{red}{2} \implies \frac{1}{0.93 \times 0.93} \implies \frac{1}{0.8649} \implies 1.1562$

$\left({0.93}^{6}\right) \left({0.93}^{-} 8\right) \cong 1.1562$