Answer:
c = 3
Step-by-step explanation:
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
note that 32 = [tex]2^{5}[/tex] and 8 = 2³ , then
[tex]32^{2c}[/tex] = [tex]8^{c+7}[/tex] , becomes
[tex](2^5)^{2c}[/tex] = [tex](2^3)^{c+7}[/tex]
[tex]2^{10c}[/tex] = [tex]2^{3c+21}[/tex]
Since the bases on both sides are equal, both 2, then equate the exponents
10c = 3c + 21 ( subtract 3c from both sides )
7c = 21 ( divide both sides by 7 )
c = 3
