Use scientific notation, the Laws of Exponents, and a calculator to perform the indicated operations. State your answer correct to the number of significant digits indicated by the given data.
$\frac{\left(3.542 \times 10^{-6}\right)^9}{\left(5.05 \times 10^4\right)^{12}}$

Solution

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Answered 1 year ago

Step 1

1 of 3

We will solve the given number, using the law of exponents and mathematical operations:

\begin{aligned} (ab)^x&=a^xb^x&&(1)\\ \frac{a^x}{a^y}&=a^{x-y}~\text{or}~a^{y-x}&&(2) \end{aligned}

Let's apply law $1$ :

\begin{aligned} \frac{(3.542\times 10^{-6})^9}{(5.05\times 10^4)^{12}}&=\frac{(3.542)^9\times 10^{-6\cdot 9}}{(5.05)^{12}\times 10^{4\cdot 12}}\\ &=\frac{(3.542)^9\times10^{-54}}{(5.05)^{12}\times 10^{48}}\\ &=\frac{87,747.95658\times 10^{-54}}{275,103,767.1\times 10^{48}}\\ &=\frac{8.774795658\times 10^4\times 10^{-54}}{2.751037671\times 10^8\times10^{48}}\\ &=\frac{8.774795658\times 10^{-50}}{2.751037671\times10^{56}}\\ \end{aligned}

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