What is the value of (6y)^3 in simplest form?

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Multiple Choice

What is the value of (6y)^3 in simplest form?

Explanation:
When you raise a product to a power, the exponent applies to each factor: (ab)^n = a^n b^n. So (6y)^3 = 6^3 · y^3 = 216 y^3. That’s the simplest form because the coefficient is cubed (6^3 = 216) and the variable is also cubed (y^3). The other forms don’t match this rule: a term like 36 y^3 would come from squaring the coefficient while leaving y cubed, which isn’t correct for a cube; a term like 216 y would be cubing the coefficient but not the y, which is also incorrect; and a term like 36 y would have neither part properly cubed. The correct result is 216 y^3.

When you raise a product to a power, the exponent applies to each factor: (ab)^n = a^n b^n. So (6y)^3 = 6^3 · y^3 = 216 y^3. That’s the simplest form because the coefficient is cubed (6^3 = 216) and the variable is also cubed (y^3). The other forms don’t match this rule: a term like 36 y^3 would come from squaring the coefficient while leaving y cubed, which isn’t correct for a cube; a term like 216 y would be cubing the coefficient but not the y, which is also incorrect; and a term like 36 y would have neither part properly cubed. The correct result is 216 y^3.

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