Which expression equals (2x)^3 after applying the exponent to both factors?

Which expression equals (2x)^3 after applying the exponent to both factors?

• A. 8x^3
• B. 6x^3
• C. 4x^3
• D. 2x^3

Answer: (A)

When you raise a product to a power, you apply the exponent to each factor. So for (2x)^3, you multiply the 2 and the x by themselves three times: (2x)(2x)(2x) = 2^3 · x^3 = 8x^3. This is the correct result because the exponent distributes to both parts of the product. If you only cube the x part or forget to cube the 2, you’d get expressions like 2x^3, which don’t reflect cubing both factors. So the expression that matches cubing both factors is 8x^3.

When you raise a product to a power, you apply the exponent to each factor. So for (2x)^3, you multiply the 2 and the x by themselves three times: (2x)(2x)(2x) = 2^3 · x^3 = 8x^3. This is the correct result because the exponent distributes to both parts of the product.

If you only cube the x part or forget to cube the 2, you’d get expressions like 2x^3, which don’t reflect cubing both factors. So the expression that matches cubing both factors is 8x^3.