Complete the Expression: (ax/7)^6 Algebraic Fraction Power

Insert the corresponding expression:

$\left(\frac{a\times x}{7}\right)^6=$

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 raised to the same power (N)

00:12 We will apply this formula to our exercise

00:17 According to the laws of exponents when a product is raised to the power (N)

00:21 it is equal to each factor in the product separately raised to the same power (N)

00:26 We will apply this formula to our exercise

00:32 This is the solution

Step-by-Step Solution

To solve this problem, we'll utilize the properties of exponents to simplify the expression $\left(\frac{a \times x}{7}\right)^6$ .

Let's proceed with the steps:

Step 1: Utilize the exponent rule for fractions: $\left( \frac{m}{n} \right)^p = \frac{m^p}{n^p}$ . This allows us to express the given expression as:

$\left(\frac{a \times x}{7}\right)^6 = \frac{(a \times x)^6}{7^6}$

Step 2: Apply the exponent rule to the multinomial in the numerator: $(a \times x)^6 = a^6 \times x^6$ .

Thus, we have:

$\frac{(a \times x)^6}{7^6} = \frac{a^6 \times x^6}{7^6}$

Conclusion: The correct expression is $\frac{a^6 \times x^6}{7^6}$ , which corresponds to choice 4.