Expand (a×b)³: Converting Product to Cube Expression

Insert the corresponding expression:

$\left(a\times b\right)^3=$

To solve the problem $\left(a \times b\right)^3$, we'll apply the rules of exponents, specifically the Power of a Product rule.

• Step 1: Understand the Power of a Product Rule
  The Power of a Product rule states that when you raise a product to an exponent, you can apply the exponent to each factor inside the parentheses individually. Mathematically, this is expressed as: $\left(a \times b\right)^n = a^n \times b^n$

• Step 2: Apply the Rule to the Given Expression
  Given the expression $\left(a \times b\right)^3$, we can apply the Power of a Product rule by raising each factor inside the parentheses to the power of 3: $\left(a \times b\right)^3 = a^3 \times b^3$

• Step 3: Simplify the Expression
  After applying the exponent to both $a$ and $b$, the expression simplifies to: $a^3 \times b^3$

Therefore, the corresponding expression for $\left(a \times b\right)^3$ is $a^3 \times b^3$.