What exponent would make the two expressions equivalent: (16x)6=(1618)?(1 point)
In order to make the two expressions equivalent, we need to find an exponent that, when applied to 16x, gives us (16x) raised to that exponent.
Let's break it down step by step:
(16x)^6 means we are multiplying (16x) by itself six times: (16x)(16x)(16x)(16x)(16x)(16x).
(16^6)(x^6) means we are raising 16 to the power of 6 and multiplying it by x raised to the power of 6: 16^6 * x^6.
To make the two expressions equivalent, we need to find the exponent that gives us the same result as (16^6 * x^6).
For this, we need to find an exponent that, when applied to 16x, will give us the same result as raising 16 to the power of 6 and multiplying it by x raised to the power of 6.
The answer is 3 because when you multiply 16x by itself three times, you get (16x)(16x)(16x) = 16^6 * x^6.
So, the exponent that would make the two expressions equivalent is 3.
The exponent that would make the two expressions equivalent is 3. When (16x)^6 is expanded, it becomes (16^6)(x^6). The number 16 raised to the power of 6 is equal to 16777216. So, we can rewrite the first expression as 16777216(x^6). 16^18 is equal to 1073741824. In order for the two expressions to be equivalent, 1073741824 must be multiplied by x^3.
explain it in a easier way
To determine the exponent that would make the two expressions equivalent, we need to set the bases equal to each other and compare the exponents.
Let's equate the bases:
16x = 16^18
Since the bases are equal, we can set the exponents equal to each other:
6 = 18
However, 6 is not equal to 18. Therefore, there is no exponent that would make the two expressions equivalent.
To find the exponent that would make the two expressions equivalent, we need to set up an equation where the bases are the same and solve for the exponent.
In this case, the base is 16 and we need to find the exponent.
The given expression is (16x)^6
On the other hand, we have (16^a)(18^b)
Since we are looking for the exponent that makes the two expressions equivalent, we need to equate the bases:
16^6 = 16^a
This equation states that the base 16 is raised to the power of 6 in both expressions.
Solving for 'a' in this case:
6 = a
Therefore, the exponent that would make the two expressions equivalent is 6.