Solve (2×3)/(7×9) Raised to the 7th Power: Complete Solution

Insert the corresponding expression:

$\left(\frac{2\times3}{7\times9}\right)^7=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a fraction raised to the power (N)

00:07 equals the numerator and denominator, each raised to the same power (N)

00:12 Note that both the numerator and denominator are products

00:16 We'll apply this formula to our exercise, making sure to use parentheses

00:23 According to the laws of exponents, a product raised to a power (N)

00:28 equals the product of each factor raised to that power (N)

00:32 We'll apply this formula to our exercise

00:39 This is the solution

Step-by-Step Solution

To solve this problem, we'll rewrite the expression using the rules of exponents.

Step 1: Identify the initial expression as $\left(\frac{2 \times 3}{7 \times 9}\right)^7$ .
Step 2: Apply the rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ to distribute the exponent of 7 to both the numerator and denominator.
Step 3: Rewrite the expression as $\frac{(2 \times 3)^7}{(7 \times 9)^7}$ .
Step 4: Apply the exponent rule $(ab)^n = a^n \times b^n$ to both the numerator and the denominator.

Following these steps, we can express:

$\frac{(2 \times 3)^7}{(7 \times 9)^7} = \frac{2^7 \times 3^7}{7^7 \times 9^7}$ .

Therefore, the correct answer is $\frac{2^7 \times 3^7}{7^7 \times 9^7}$ , which corresponds to choice 3.