Let's answer your questions one by one:
Question 3
To rewrite \( \sqrt[4]{23} \), we can express it in terms of a rational exponent. The fourth root of a number can be written as that number raised to the power of \( \frac{1}{4} \). So:
\[ \sqrt[4]{23} = 23^{\frac{1}{4}} \]
Question 4
To rewrite \( 9^{13} \) using a root, you can express it in terms of a fraction with a root. One way to do this is to introduce a root and use properties of exponents. For example, you could write:
\[ 9^{13} = (9^1)^{13} = 9^{\frac{26}{2}} = \sqrt{(9^{26})} \]
So, one possible rewriting is:
\[ 9^{13} = \sqrt{9^{26}} \]
Question 5
To simplify \( 27^{13} \), first express 27 as a power of a prime number. Since \( 27 = 3^3 \), we can rewrite \( 27^{13} \) as:
\[ (3^3)^{13} = 3^{3 \cdot 13} = 3^{39} \]
So, the simplified form of \( 27^{13} \) is:
\[ 27^{13} = 3^{39} \]
If you need further clarifications or assistance with different types of problems, feel free to ask!