Question

What rational number could be used as an exponent to rewrite 23−−√4
?(1 point)

Answer 1

To rewrite \( \sqrt[4]{23} \) in exponential form, we can express it using rational exponents.

The fourth root of \( 23 \) can be expressed as:

\[
\sqrt[4]{23} = 23^{1/4}
\]

So the rational number that could be used as an exponent to rewrite \( \sqrt[4]{23} \) is \( \frac{1}{4} \).

Answer 2

How can you rewrite 9^1/3
using a root?(1 point)

Answer 3

To rewrite \( 9^{1/3} \) using a root, we can express it as a cube root.

The expression \( 9^{1/3} \) can be rewritten as:

\[
\sqrt[3]{9}
\]

So, \( 9^{1/3} \) is equal to \( \sqrt[3]{9} \).

Answer 4

What is the simplified form of 27^1/3
?(1 point)

Answer 5

To simplify \( 27^{1/3} \), we can find the cube root of \( 27 \).

Since \( 27 = 3^3 \), we have:

\[
27^{1/3} = (3^3)^{1/3}
\]

Using the property of exponents \((a^m)^n = a^{m \cdot n}\):

\[
(3^3)^{1/3} = 3^{3 \cdot \frac{1}{3}} = 3^1 = 3
\]

Therefore, the simplified form of \( 27^{1/3} \) is \( 3 \).