Solve the following equation 6^2m × 4^-m÷ (3^m)^2

asked Apr 21, 2022 5.9k views

1 vote

Solve the following equation
6^2m × 4^-m÷ (3^m)^2

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8 votes

Answer:

Explanation:

6^2m × 4^-m÷ (3^m)^2 =
$(6^(2m) * 4^(-m))/((3^(m))^(2))\\$

$= ((3*2)^(2m)*(2^(2))^(-m))/(3^(2*m))\\\\=(3^(2m)*2^(2m)*2^(-2m))/(3^(2m))\\\\\\=3^(2m-2m)*2^(2m-2m)\\\\=3^(0)*2^(0)\\\\=1*1\\= 1$

Hint:

$a^(m)*a^(n)= a^(m+n)\\\\(a^(m))^(n)=a^(m*n)\\\\(a^(m))/(a^(n))=a^(m-n)$

Nat Wallbank answered Apr 26, 2022

5.7k points

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