https://file.aiquickdraw.com/mathbot/file/1729032417183jxdbsh6h.jpg

The expression shown in the image is:

\[
\sqrt[8]{10^3}
\]

To write this as an exponential expression, we use the rule that a radical expression can be converted into an exponent by expressing the root as a fraction. Specifically, the \(n\)-th root of a number \(x^m\) is written as \(x^{\frac{m}{n}}\).

For this case, we have:

\[
\sqrt[8]{10^3} = 10^{\frac{3}{8}}
\]

So the expression written as an exponential is:

\[
10^{\frac{3}{8}}
\]

Would you like further details or clarifications on this? 

Here are five follow-up questions to deepen your understanding:

1. How do you convert a general radical expression into exponential form?
2. What is the relationship between radicals and fractional exponents?
3. How would the expression change if the exponent inside the radical were different?
4. What happens if the radical order (like the 8th root) is changed to a different number?
5. Can you evaluate \(10^{\frac{3}{8}}\) as a decimal approximation?

**Tip:** Always remember that the nth root corresponds to an exponent of \(\frac{1}{n}\), and you can multiply exponents when taking roots of powers.

Write the following as an exponential expression: 8th root of 10 raised to the power of 3.

Learn how to convert the 8th root of 10 raised to the power of 3 into an exponential expression using the fractional exponent rule. Understand the relationship between radicals and exponents with detailed steps. Suitable for Grades 8-10.

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