Question

Insert the correct symbol $>,<$ or $=$ in the boxes provided in each of the following cases.
$\begin{array}{c}\left(a\right)2^4{4}^2\\ \left(b\right)3^9{9}^3\\ \left(c\right)7^2{2}^7\\ \left(d\right)3^4{9}^2\\ \left(e\right)4^6{6}^4\\ \left(f\right)4^9{8}^4\end{array}$

Answer 1

$\begin{array}{c}a)2^4{4}^2\Rightarrow 2^4{\left(2^2\right)}^2\Rightarrow 2^4=2^4\\ \left(b\right)3^9{9}^3\Rightarrow 3^9{\left(3^2\right)}^3\Rightarrow 3^9>3^6\\ \left(c\right)7^2{2}^7\Rightarrow 49<128\\ \left(d\right)3^4{9}^2\Rightarrow 3^4{\left(3^2\right)}^2\Rightarrow 3^4=3^4\\ \left(e\right)4^6{6}^4\Rightarrow {\left(2^2\right)}^6{\left(3\times 2\right)}^4\Rightarrow 2^{12}{3}^4\times 2^4\Rightarrow 2^4\times 2^8{3}^4\times 2^4\Rightarrow 2^8>3^4\\ \left(f\right)4^9{8}^4\Rightarrow {\left(2^2\right)}^9{\left(2^3\right)}^4\Rightarrow 2^{18}>2^{12}\end{array}$