Evaluate (5×6×7)/(9×11×13) Raised to Power b: Complex Fraction Expression

Insert the corresponding expression:

$\left(\frac{5\times6\times7}{9\times11\times13}\right)^b=$

To solve this problem, we'll use exponentiation properties to simplify the given expression:

• Step 1: Apply the exponent to each term in the numerator: $(5 \times 6 \times 7)^b = 5^b \times 6^b \times 7^b$.
• Step 2: Apply the exponent to each term in the denominator: $(9 \times 11 \times 13)^b = 9^b \times 11^b \times 13^b$.
• Step 3: Use the property of exponents for fractions: $\left(\frac{5 \times 6 \times 7}{9 \times 11 \times 13}\right)^b = \frac{5^b \times 6^b \times 7^b}{9^b \times 11^b \times 13^b}$.

As we have followed the rules of exponents and simplified accordingly, the corresponding expression is:

$\frac{5^b \times 6^b \times 7^b}{9^b \times 11^b \times 13^b}$.