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

Video Solution

Solution Steps

00:12 Let's simplify this problem together.

00:15 The power law tells us that a fraction raised to the power, N, means both the top and bottom are raised to power N.

00:23 Remember, the power has an addition in it.

00:26 We'll use this rule for our problem.

00:33 If a product is raised to a power, N, each part is raised to power N separately.

00:39 Let's apply this rule to our task.

00:42 And there you have it. That's our 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.