Simplify the Expression: x⁷ × 9⁷ × y⁷ Using Exponent Properties

Insert the corresponding expression:

$x^7\times9^7\times y^7=$

To solve the problem, we will use the Power of a Product rule as described:

• Step 1: Recognize that each factor $x$, $9$, and $y$ is raised to the power of 7 in the expression $x^7 \times 9^7 \times y^7$.
• Step 2: Apply the exponent rule which states $(a \times b \times c)^n = a^n \times b^n \times c^n$.
• Step 3: Rewrite the given expression as a single term raised to the 7th power: $(x \times 9 \times y)^7$.

This step successfully combines all the individual terms under one exponent using the rule. Therefore, the expression simplifies to:

$(x \times 9 \times y)^7$

Upon examining the choices, the corresponding expression matches the option $\left(x \times 9 \times y\right)^7$.

Thus, the correct solution to the problem is $\left(x \times 9 \times y\right)^7$.