Answer :

Let's simplify the expression [tex]\(\left(\frac{2}{3}\right)^2 \times \left(\frac{2}{3}\right)^3\)[/tex].

### Step-by-Step Solution:

1. Identify the base and exponents:

Both terms [tex]\(\left(\frac{2}{3}\right)^2\)[/tex] and [tex]\(\left(\frac{2}{3}\right)^3\)[/tex] share the same base, which is [tex]\(\frac{2}{3}\)[/tex].

2. Apply the laws of exponents:

When multiplying expressions with the same base, you add the exponents.
[tex]\[ \left(\frac{2}{3}\right)^2 \times \left(\frac{2}{3}\right)^3 = \left(\frac{2}{3}\right)^{2+3} \][/tex]

3. Simplify the exponent:

Add the exponents:
[tex]\[ 2 + 3 = 5 \][/tex]

So,
[tex]\[ \left(\frac{2}{3}\right)^{2+3} = \left(\frac{2}{3}\right)^5 \][/tex]

4. Calculate the results of the individual fractions:

Let's calculate each part separately:
[tex]\[ \left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9} \approx 0.4444 \][/tex]
and
[tex]\[ \left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{8}{27} \approx 0.2963 \][/tex]

5. Calculate the final simplified expression:

Raise [tex]\(\left(\frac{2}{3}\right)\)[/tex] to the power of 5:
[tex]\[ \left(\frac{2}{3}\right)^5 = \frac{2^5}{3^5} = \frac{32}{243} \approx 0.1317 \][/tex]

### Final Result:
- [tex]\(\left(\frac{2}{3}\right)^2 \approx 0.4444\)[/tex]
- [tex]\(\left(\frac{2}{3}\right)^3 \approx 0.2963\)[/tex]
- [tex]\(\left(\frac{2}{3}\right)^5 \approx 0.1317\)[/tex]

Thus, the simplified result of [tex]\(\left(\frac{2}{3}\right)^2 \times \left(\frac{2}{3}\right)^3\)[/tex] is approximately [tex]\(0.1317\)[/tex].