Simplify (3r)^3

Simplify (3r)^3

• A. 27r^3
• B. 9r^3
• C. 3r^3
• D. 81r^3

Answer: (A)

When you raise a product to a power, apply the exponent to every factor inside the parentheses. So (3r)^3 means (3r)(3r)(3r). Multiply the numeric parts together and the variable parts together: 3×3×3 = 27 and r×r×r = r^3. This gives 27r^3, which is why the correct result is 27r^3. The other options come from applying the exponent incorrectly: squaring the 3 would give 9r^3, forgetting to cube the 3 would give 3r^3, and mixing up the powers would lead to 81r^3, which isn’t correct for a cube.

When you raise a product to a power, apply the exponent to every factor inside the parentheses. So (3r)^3 means (3r)(3r)(3r). Multiply the numeric parts together and the variable parts together: 3×3×3 = 27 and r×r×r = r^3. This gives 27r^3, which is why the correct result is 27r^3.

The other options come from applying the exponent incorrectly: squaring the 3 would give 9r^3, forgetting to cube the 3 would give 3r^3, and mixing up the powers would lead to 81r^3, which isn’t correct for a cube.