Simplified expression

8
__
8^2/3

1 answer

To simplify the expression \( \frac{8}{8^{2/3}} \), we can use the properties of exponents.

First, we rewrite the numerator and the denominator:

  1. The numerator is \( 8 \), which can be written as \( 8^1 \).
  2. The denominator is \( 8^{2/3} \).

Now we can rewrite the expression as:

\[ \frac{8^1}{8^{2/3}} = 8^{1 - 2/3} \]

To simplify the exponent:

\[ 1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3} \]

Thus, we have:

\[ 8^{1 - 2/3} = 8^{1/3} \]

Now, \( 8^{1/3} \) represents the cube root of 8:

\[ 8^{1/3} = \sqrt[3]{8} = 2 \]

Therefore, the simplified expression is:

\[ \boxed{2} \]