Solve for the Expression: (5×6×7/9)^(2x+1)

Video Solution

Solution Steps

00:00 Simplify the following problem

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

00:08 equals the numerator and denominator raised to the same power (N)

00:12 Note that the power contains an addition operation

00:15 We will apply this formula to our exercise

00:21 According to the power laws when a product is raised to the power (N)

00:24 it is equal to each factor in the product separately raised to the same power (N)

00:29 We will apply this formula to our exercise

00:39 This is the solution

Step-by-Step Solution

Let's solve the problem step-by-step:

We begin with the expression: $\left(\frac{5 \times 6 \times 7}{9}\right)^{2x+1}$ .

Step 1: Apply the exponent to both the numerator and the denominator using the rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ .

This gives: $\frac{(5 \times 6 \times 7)^{2x+1}}{9^{2x+1}}$ , as in choice b.

Step 2: Distribute the exponent across each factor in the numerator: $(a \times b \times c)^n = a^n \times b^n \times c^n$ .

This results in: $\frac{5^{2x+1} \times 6^{2x+1} \times 7^{2x+1}}{9^{2x+1}}$ .

Therefore, the expression $\left(\frac{5\times6\times7}{9}\right)^{2x+1}$ evaluates to:

$\frac{5^{2x+1} \times 6^{2x+1} \times 7^{2x+1}}{9^{2x+1}}$ .

This corresponds to choice 1. Hence, choices a' and b' are equivalent.

The correct answer is: a'+b' are correct.