What exponent would make the two expressions equivalent: (16x)6=(16,18)?

Answer 1

To find the exponent that would make the two expressions equivalent, we need to determine a value for x that satisfies the equation.

First, let's simplify the left side of the equation:
(16x)^6 = 16^6 * x^6 = 16^6 * x^6

Now let's simplify the right side of the equation:
(16,18) = 16,18 = 16 * 18 = 288

Setting the simplified expressions equal to each other, we have:
16^6 * x^6 = 288

To solve for x, we need to isolate it. Dividing both sides of the equation by 16^6:
x^6 = 288 / 16^6

Now we need to take the sixth root of both sides:
x = (288 / 16^6)^(1/6)

Calculating this value gives x ≈ 1.241.

Therefore, the exponent that makes the two expressions equivalent is 1.241.