Calculate (10×3)⁴: Fourth Power of a Product Expression

Video Solution

Solution Steps

00:00 Simplify the following expression

00:03 We'll simplify in 2 different ways, first we'll solve the parentheses

00:08 This is one way

00:12 Now let's see the second way of simplification

00:16 In order to open parentheses with an exponent over multiplication

00:20 We raise each factor to the power

00:24 We'll use this formula in our exercise

00:30 In multiplication, the order of factors doesn't matter

00:35 Therefore, both expressions are equal

00:38 We'll use this formula in our exercise and switch the factors

00:45 Again we'll use the formula in order to simplify the power of multiplication

00:51 This is the solution to the problem

Step-by-Step Solution

To solve this problem, we'll apply the power of a product rule to the expression $(10 \times 3)^4$ .

Step 1: Identify the expression.
The given expression is $(10 \times 3)^4$ .
Step 2: Apply the power of a product law.
According to the rule, $(a \times b)^n = a^n \times b^n$ , our expression becomes:
$(10 \times 3)^4 = 10^4 \times 3^4$ .
Step 3: Evaluate the choices:
- First choice: $3^4 \times 10^4$
Rearranging terms, this is equivalent to $10^4 \times 3^4$ . Therefore, it matches our transformed expression.
- Second choice: $30^4$
Since $30 = 10 \times 3$ , $(10 \times 3)^4 = 30^4$ . This simplifies to the same expression.
- Third choice: $10^4 \times 3^4$
Therefore, the solution is that all answers are correct.