Pregunta
6. Express in power form: \( \frac{5}{7} \times \frac{5}{7} \times \frac{5}{7} \times \frac{5}{7} \times \frac{5}{7} \)
Ask by Byrd Moran. in Papua New Guinea
Mar 18,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The expression in power form is \( \left(\frac{5}{7}\right)^5 \).
Solución
1. The given product is
\[
\frac{5}{7} \times \frac{5}{7} \times \frac{5}{7} \times \frac{5}{7} \times \frac{5}{7}.
\]
2. Notice that the factor \(\frac{5}{7}\) is repeated 5 times.
3. When the same number is multiplied by itself multiple times, it can be written in power form. Thus, we have
\[
\left(\frac{5}{7}\right)^5.
\]
4. Therefore, the expression in power form is
\[
\left(\frac{5}{7}\right)^5.
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Bonus Knowledge
When you multiply the same number together multiple times, you can express it in power form. In this case, you are multiplying \( \frac{5}{7} \) a total of 5 times. You can write this as \( \left( \frac{5}{7} \right)^5 \). Furthermore, remember that powers have great utility in simplifying expressions. For instance, writing in power form not only makes calculations more manageable but also helps in understanding concepts like exponential growth in mathematics. It’s a handy tool!

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