What exponent would make the two expressions equivalent: (16x)6=(16,18)?
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.
To find the exponent that would make the two expressions equivalent, we need to set the exponents equal to each other and solve for the unknown exponent.
In the first expression, we have (16x)^6, which means we raise the entire expression (16x) to the power of 6.
In the second expression, we have (16,18), which is not clear if it is a multiplication or a summation.
If it is a multiplication, then we have 16 times 18, which equals 288.
So, our equation becomes (16x)^6 = 288.
To find the exponent that would make this equation true, we need to take the sixth root of both sides of the equation.
∛[(16x)^6] = ∛288
Simplifying, we have:
16x = ∛288
Dividing both sides by 16, we get:
x = (∛288)/16
Taking the cube root of 288, we get:
x = 2/(2∛2) = (∛2)/∛2 = 1
Therefore, x = 1 is the value that would make the two expressions (16x)^6 and (16,18) equivalent, assuming (16,18) represents multiplication.
To find the exponent that makes the two expressions equivalent, we can set up an equation and solve for the exponent.
The equation is: (16x)^n = (16,18)
First, let's simplify (16x)^6:
(16x)^6 = (16^6)(x^6) = 16^6x^6 = 16777216x^6
Now we have:
16777216x^6 = (16,18)
To solve for x, we need to isolate it. Divide both sides of the equation by 16777216:
x^6 = (16,18) / 16777216
Since the value (16,18) is not clearly defined, we cannot compute this further.