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

Insert the corresponding expression:

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

Video Solution

Solution Steps

00:00 Simplify the following problem

00:04 According to the laws of exponents, a fraction raised to the power (N)

00:09 equals the numerator and denominator raised to the same power (N)

00:13 Note that both numerator and denominator are products

00:17 We will apply this formula to our exercise

00:22 According to the laws of exponents when the entire product is raised to the power (N)

00:26 it is equal to each factor in the product separately raised to the same power (N)

00:32 We will apply this formula to our exercise

00:48 This is the solution

Step-by-Step Solution

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:

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