Question

Select the equivalent expression (4^3y)³

Choose 1
A.4⁶/y4
B.4⁹/y³
C.4⁹/y
D.4⁶/y³

Answer 1

The correct expression equivalent to (4^3y)^3 is 4^9/y^3, as we cube the numeric term and multiply the exponent by 3.

Step-by-step explanation:

The expression we are dealing with is (4^3y)^3. When cubing of exponentials occurs, we need to cube the numeric term and multiply the exponent by 3. The principle is that when we raise a power to a power, we multiply the exponents. Therefore, (4^3)^3 becomes 4^(3*3) since the y is also an exponent, we apply the same operation to it: (y^3). Combining both, we have 4^(3*3) multiplied by y^(3*1), which simplifies to 4^9 times y^3. The correct expression is 4^9/y^3.