What is 2/3 x 2/3 x 2/3 x 2/3 in fraction form

What is 2/3 x 2/3 x 2/3 x 2/3 in fraction form

The Correct Answer and Explanation is :

The correct answer is: frac{16}{81}

The calculation of ( \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} ) involves multiplying four fractions together.

Here is the step-by-step process:

1. Multiplying the numerators (top numbers):

• ( 2 \times 2 \times 2 \times 2 = 16 )

1. Multiplying the denominators (bottom numbers):

• ( 3 \times 3 \times 3 \times 3 = 81 )

So, ( \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{16}{81} ).

Explanation:

When multiplying fractions, the process is straightforward: you multiply the numerators together and the denominators together. Here, each fraction is ( \frac{2}{3} ), so we multiply the four numerators (all 2s) and the four denominators (all 3s).

1. Numerators: In the fraction ( \frac{2}{3} ), the numerator is 2. So when multiplying four fractions, we get ( 2 \times 2 \times 2 \times 2 = 16 ).
2. Denominators: The denominator in ( \frac{2}{3} ) is 3. Similarly, multiplying the four denominators gives us ( 3 \times 3 \times 3 \times 3 = 81 ).

The result is ( \frac{16}{81} ), which is already in its simplest form because 16 and 81 have no common factors other than 1.

This process works for any set of fractions—multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. Fractions often simplify after multiplication, but in this case, 16 and 81 do not share any divisors, so the fraction cannot be reduced further.

Thus, ( \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{16}{81} ).