Let's solve the given expression step by step:

You have: $\left( \frac{2}{3} \right)^5 \times \left( \frac{2}{3} \right)^5 = \left( \frac{2}{3} \right)$

Step 1: Simplifying the Left-Hand Side

Using the property of exponents, when you multiply powers with the same base, you add the exponents: $\left( \frac{2}{3} \right)^5 \times \left( \frac{2}{3} \right)^5 = \left( \frac{2}{3} \right)^{5+5} = \left( \frac{2}{3} \right)^{10}$

Step 2: Equating to the Right-Hand Side

Now, equate it to the right-hand side: $\left( \frac{2}{3} \right)^{10} = \left( \frac{2}{3} \right)$

Step 3: Compare Exponents

Since the bases are the same, you can compare the exponents: $10 = 1$ This is clearly not true, so the equation cannot hold as given. Therefore, the equation is incorrect.

Would you like a more detailed explanation, or do you have any further questions?

Related Questions:

1. What are the rules for multiplying powers with the same base?
2. How do you simplify expressions involving exponents?
3. Can fractional exponents be handled similarly to integer exponents?
4. How do you solve equations that involve exponents with different bases?
5. What is the general form for multiplying powers?

Tip:

When dealing with powers of fractions, apply the same exponent rules as you would for whole numbers—focus on simplifying the base first.