7^2/7^? = 7^19
To solve the equation, we can use the property of exponents that states: When dividing two numbers with the same base, subtract the exponents.
So, we can rewrite the equation as:
7^(2 - ?) = 7^19
Now, since the bases are the same, the exponents must be equal. Therefore, we have:
2 - ? = 19
To isolate the variable "?", we can subtract 2 from both sides:
-? = 19 - 2
-? = 17
To solve for "?", we multiply both sides by -1:
-1 * -? = -1 * 17
? = -17
Therefore, 7^2/7^(-17) = 7^19.
To solve this equation step-by-step, we can use the properties of exponents:
First, simplify both sides of the equation:
On the left side, we have (7^2) / (7^?). According to the rule of division with the same base, we subtract the exponents:
7^(2 - ?).
On the right side, we have 7^19.
Now we can set the exponents equal to each other:
2 - ? = 19.
To isolate ?, we need to solve for it:
Subtract 2 from both sides:
-? = 19 - 2,
-? = 17.
Multiply both sides by -1 to get rid of the negative sign:
? = -17.
So, the value of ? in the equation (7^2) / (7^?) = 7^19 is -17.
To solve this equation, we need to find the value of the exponent "?" that makes the equation true.
We can start by using a simple property of exponents, which states that when you divide two numbers with the same base, you subtract their exponents. In other words, for any positive numbers a and b, a^(n-m) = a^n / a^m.
Using this property, we can rewrite the equation as 7^2 / 7^? = 7^19 becomes 7^(2-?) = 7^19.
Since the bases are the same, 7, we can drop the bases and equate the exponents:
2 - ? = 19
To find the value of "?", we can isolate it by subtracting 2 from both sides:
-? = 19 - 2
Simplifying further:
-? = 17
Now, to solve for "?", we can multiply both sides of the equation by -1 to cancel out the negative sign:
? = -17
Therefore, the value of "?" that makes the equation 7^2 / 7^? = 7^19 true is "? = -17".