What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12?

Answer 1

To solve the equation $\frac{7^{?}}{7^5}=7^{12}$, we can use the properties of exponents. According to the rules of exponents, when dividing two expressions with the same base, you subtract their exponents:

$$\frac{7^m}{7^n}=7^{m-n}$$

Applying this to our equation gives us:

$$\frac{7^{?}}{7^5}=7^{?-5}$$

Set this equal to $7^{12}$:

$$7^{?-5}=7^{12}$$

Since the bases are the same, we can equate the exponents:

$$?-5=12$$

To find the value of $?$, we add 5 to both sides:

$$?=12+5=17$$

Thus, the missing number is:

$$\boxed{{\displaystyle 17}}$$