Evaluate the expression 21/16 x 12/35 x 32/45 reduced to lowest terms.

To evaluate the expression ( \frac{21}{16} \times \frac{12}{35} \times \frac{32}{45} ) and reduce it to its lowest terms, one can follow several steps that involve simplifying the fractions.

First, multiply the numerators together and the denominators together:

[

\text{Numerator: } 21 \times 12 \times 32

]

[

\text{Denominator: } 16 \times 35 \times 45

]

Calculating each:

• Numerator:

• ( 21 ) can be factored as ( 3 \times 7 ),

• ( 12 ) can be factored as ( 3 \times 4 = 3 \times 2^2 ),

• ( 32 ) can be factored as ( 2^5 ).

Putting it all together, the numerator becomes:

[

3 \times 7 \times 3 \times 2^2 \times 2^5 = 3^2 \times 7 \times 2^7

]

• Denominator:

• ( 16 = 2^