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

Video Solution

Solution Steps

00:08 Let's simplify this expression together.

00:11 We'll try two different methods. First, we'll solve what's inside the parentheses.

00:18 This is the first method.

00:20 Now, let's explore the second simplification method.

00:24 To expand parentheses with an exponent over multiplication,

00:29 Raise each factor inside to the power.

00:32 We'll apply this formula in our exercise now.

00:38 Remember, in multiplication, the order of factors doesn't matter.

00:43 So, both expressions are equal.

00:46 We'll use the formula again and switch the factors accordingly.

00:53 Again, let's use the formula to simplify the exponent on multiplication.

00:59 And there you go! That's how we solve this 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.