Simplify (x³)² × y⁵/y³: Step-by-Step Exponent Reduction

To solve the problem of reducing the expression $\frac{\left(x^3\right)^2 \times y^5}{y^3}$, we'll follow these steps:

• Step 1: Simplify $\left(x^3\right)^2$ using the power of a power rule.

• Step 2: Simplify the expression using the division rule for $y^5$ divided by $y^3$.

Let's execute these steps:

Step 1: Apply the power of a power rule to $\left(x^3\right)^2$.

According to the power of a power rule, $(x^m)^n = x^{m \cdot n}$.

So, $\left(x^3\right)^2 = x^{3 \cdot 2} = x^6$.

Step 2: Simplify the division of exponents for the $y$ variable.

The expression now looks like $\frac{x^6 \times y^5}{y^3}$.

Using the division rule for exponents, $y^m / y^n = y^{m-n}$, we get:

$y^5 / y^3 = y^{5-3} = y^2$.

Final Expression: Combining the results from Step 1 and Step 2, we obtain:

$x^6 \times y^2$.

Therefore, the solution to the problem is $x^6 \times y^2$.