if (36^{12 - m}=6^{2m}), what is the value of (m)?\n4\n6\n8\n9

Answer

Explanation:

Step1: Rewrite 36 as 6^2

Since (36 = 6^2), then (36^{12 - m}=(6^2)^{12 - m}). According to the power - of - a - power rule ((a^b)^c=a^{bc}), so ((6^2)^{12 - m}=6^{2(12 - m)}).

Step2: Set exponents equal

The original equation (36^{12 - m}=6^{2m}) becomes (6^{2(12 - m)} = 6^{2m}). If (a^x=a^y), then (x = y). So (2(12 - m)=2m).

Step3: Expand the left - hand side

Expand (2(12 - m)) using the distributive property (a(b - c)=ab - ac). We get (24-2m = 2m).

Step4: Solve for m

Add (2m) to both sides of the equation: (24-2m + 2m=2m+2m), which simplifies to (24 = 4m). Then divide both sides by 4: (m=\frac{24}{4}=6).