WHAT EXPONENT WOULD MAKE THE TWO EXPRESSIONS EQUIVALENT: (16^x)^6 = (16^18)?
To find the exponent that would make the two expressions equivalent, we must equate the exponents on both sides of the equation.
(16^x)^6 = (16^18)
Since the base on both sides is 16, we can equate the exponents:
6x = 18
To solve for x, we divide both sides of the equation by 6:
x = 3
Therefore, the exponent that would make the two expressions equivalent is x = 3.
To determine the exponent that would make the two expressions equivalent, we need to find the value of x in the equation (16^x)^6 = (16^18).
Step 1: Simplify the left side of the equation.
The expression (16^x)^6 can be rewritten as 16^(x * 6), using the property (a^b)^c = a^(b * c). Therefore, the equation becomes 16^(6x) = 16^18.
Step 2: Since the bases are the same (16), we can set the exponents equal to each other.
Thus, we have 6x = 18.
Step 3: Solve for x.
To find x, we divide both sides of the equation by 6:
6x/6 = 18/6.
This simplifies to x = 3.
Therefore, the exponent that would make the two expressions equivalent is x = 3.
To determine the exponent that would make the two expressions equivalent, you need to solve for the value of "x" in the equation (16^x)^6 = 16^18. Here's how you can approach it:
Step 1: Recall the exponent property (a^m)^n = a^(m*n). Apply this property to the left side of the equation: (16^x)^6 = 16^(x*6).
Step 2: Simplify the equation: 16^(x*6) = 16^18.
Step 3: Since the base on both sides of the equation is the same (16), the exponents must be equal. Therefore, we can set x * 6 = 18.
Step 4: Solve for x by dividing both sides of the equation by 6:
(x * 6) / 6 = 18 / 6.
x = 3.
Thus, the exponent that makes the two expressions equivalent is x = 3.