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

Insert the corresponding expression:

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

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.