Question
8/8^2/3
simplify
simplify
Answers
GPT-4o mini
To simplify the expression \( \frac{8}{8^{\frac{2}{3}}} \), we can follow these steps:
1. Rewrite \( 8 \) using exponents:
\[
8 = 2^3
\]
Thus, we can express the entire expression as:
\[
\frac{2^3}{(2^3)^{\frac{2}{3}}}
\]
2. Simplify the denominator:
\[
(2^3)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^2
\]
3. Substitute back into the expression:
\[
\frac{2^3}{2^2}
\]
4. Apply the quotient of powers rule:
\[
\frac{2^3}{2^2} = 2^{3-2} = 2^1 = 2
\]
Thus, the simplified result is:
\[
2
\]
1. Rewrite \( 8 \) using exponents:
\[
8 = 2^3
\]
Thus, we can express the entire expression as:
\[
\frac{2^3}{(2^3)^{\frac{2}{3}}}
\]
2. Simplify the denominator:
\[
(2^3)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^2
\]
3. Substitute back into the expression:
\[
\frac{2^3}{2^2}
\]
4. Apply the quotient of powers rule:
\[
\frac{2^3}{2^2} = 2^{3-2} = 2^1 = 2
\]
Thus, the simplified result is:
\[
2
\]
use the Quotient Property to simplify each expression