Question

What is 10^3 multiplied by 7^3? A. 102,700 B. 1,000,000 C. 343,000 D. 3,430

Answer 1

`\(10^3\)` multiplied by
`\(7^3\`) is equal to 343,000, therefore the correct answer is C.

Step-by-step explanation:

The expression
`\(10^3 * 7^3\)` involves exponentiation, specifically raising 10 to the power of 3 and 7 to the power of 3, and then multiplying the results. To grasp this, let's break it down:

`- \(10^3\) means \(10 * 10 * 10\), resulting in \(1,000\).`

`- \(7^3\) implies \(7 * 7 * 7\), which equals \(343\).`

Now, when we multiply
`\(1,000\) by \(343\)`, we obtain the final product:

`\[ 10^3 * 7^3 = 1,000 * 343 = 343,000 \]`

Therefore, the correct answer is 343,000, corresponding to option C. This demonstrates the fundamental principles of exponentiation and multiplication.

The process showcases the power of exponents in representing repeated multiplication efficiently. Understanding exponent rules allows us to compute the product of
`\(10^3\)` and
`\(7^3\)` accurately, resulting in 343,000. This mathematical operation exemplifies the foundational concepts that underlie more complex calculations in algebra and beyond.