What exponent would make the two expressions equivalent: (16^x)^6=(16^18) ?(1 point)
Using the property of exponentiation, we can simplify the left side of the equation:
(16^x)^6 = 16^(x * 6) = 16^(6x)
Since the right side of the equation is already in the form 16^18, we can equate the exponents:
6x = 18
To solve for x, we divide both sides of the equation by 6:
x = 18 / 6 = 3
Therefore, the correct exponent is x = 3.
To find the exponent that would make the two expressions equivalent, you need to set the exponents equal to each other.
In this case, (16^x)^6 is equal to (16^18).
So, setting the exponents equal to each other:
x * 6 = 18
Now, solving for x:
x = 18 / 6
x = 3
Therefore, the exponent that would make the two expressions equivalent is 3.
To determine the exponent that would make the two expressions equivalent, follow these steps:
Step 1: Apply the exponent rule
The rule states that when raising a power to another power, you should multiply the exponents. So applying this rule, the equation becomes:
16^(x * 6) = 16^18
Step 2: Set the exponents equal to each other
Since the base is the same (16) on each side of the equation, we can set the exponents equal to each other:
x * 6 = 18
Step 3: Solve for x
Now we can solve for x by dividing both sides of the equation by 6:
x = 18 / 6
Step 4: Simplify
Finally, simplify the expression:
x = 3
Therefore, the exponent that would make the two expressions equivalent is 3.