Answer :
To solve the equation
[tex]\[ \frac{7^{16}}{7^{12}} = \frac{7^{-18}}{?} \][/tex]
we need to simplify and balance the exponents on both sides.
First, simplify the left-hand side:
[tex]\[ \frac{7^{16}}{7^{12}} = 7^{16-12} = 7^4 \][/tex]
So, the equation becomes:
[tex]\[ 7^4 = \frac{7^{-18}}{?} \][/tex]
To balance the equation, the exponents of 7 on both sides must be equal. This means:
[tex]\[ 7^4 = 7^{-18} / ? \][/tex]
Since the bases are the same, we can set the exponents equal to each other to find the missing term:
[tex]\[ 4 = -18 / ? \][/tex]
Solve for the missing term:
[tex]\[ ? = -18 / 4 = -4.5 \][/tex]
Therefore, the missing term in the denominator is
[tex]\[ \boxed{-4.5} \][/tex]
[tex]\[ \frac{7^{16}}{7^{12}} = \frac{7^{-18}}{?} \][/tex]
we need to simplify and balance the exponents on both sides.
First, simplify the left-hand side:
[tex]\[ \frac{7^{16}}{7^{12}} = 7^{16-12} = 7^4 \][/tex]
So, the equation becomes:
[tex]\[ 7^4 = \frac{7^{-18}}{?} \][/tex]
To balance the equation, the exponents of 7 on both sides must be equal. This means:
[tex]\[ 7^4 = 7^{-18} / ? \][/tex]
Since the bases are the same, we can set the exponents equal to each other to find the missing term:
[tex]\[ 4 = -18 / ? \][/tex]
Solve for the missing term:
[tex]\[ ? = -18 / 4 = -4.5 \][/tex]
Therefore, the missing term in the denominator is
[tex]\[ \boxed{-4.5} \][/tex]
