Question

Use the order of operations to simplify. (2/7)^2. (7/9)^2 (2/7)^2. (7/9)^2 = (Simplify your answer. Type a whole number or a fraction.)

Answer 1

Answer:

$(2/7)^{2} (7/9)^{2}(2/7)^{2} (7/9)^{2} = \frac{16}{6561}$

Step-by-step explanation:

$(2/7)^{2} (7/9)^{2}(2/7)^{2} (7/9)^{2}$

1. Do what is in parenthesis first. You can distribute the exponent to both the numerator and demonitator of each fraction in order to operate.

   $\frac{2^{2} }{7^{2} } \frac{7^{2}} {9^{2} } \frac{2^{2} }{7^{2} } \frac{7^{2}} {9^{2} }$

2. Exponents (ie Powers and Square Roots, etc.)

   $\frac{4}{49} \frac{49}{81} \frac{4}{49} \frac{49}{81}$

3. Multiplication and Division (left-to-right)

    $\frac{4}{81} \frac{4}{49} \frac{49}{81}$

• since multiplication is commutative then :

       $\frac{4}{81} \frac{4}{49} \frac{49}{81}$ = $\frac{4}{49} \frac{49}{81} \frac{4}{81}$

• therefore

        $\frac{4}{49} \frac{49}{81} \frac{4}{81}$ = $\frac{4}{81} \frac{4}{81}$

So: $\frac{4}{81} \frac{4}{81}$ = $\frac{16}{6561}$