Question

Which expression is equivalent to (3x2y3)4?

Answer 1

To find the equivalent expression of (3x^2y^3)^4, we multiply each of the exponents inside the parentheses by the exponent outside, resulting in 81x^8y^12.

Step-by-step explanation:

The question asks for the equivalent expression of (3x2y3)4. According to the rules of exponents, when you raise a power to a power, you multiply the exponents. Applying this rule, we multiply the exponent outside the parenthesis by each of the exponents inside the parenthesis.

So, the equivalent expression is:

34x2×4y3×4 which simplifies to 81x8y12.

This is similar to the example where (53)4 is equal to 512, because the exponents 3 and 4 are multiplied to give us 12.