Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
{2^x} = 16\\
\Leftrightarrow {2^x} = {2^4}\\
\Leftrightarrow x = 4\\
b,\\
{\left( {\dfrac{x}{{13}}} \right)^2} = \dfrac{{49}}{{169}}\\
\Leftrightarrow \dfrac{{{x^2}}}{{169}} = \dfrac{{49}}{{169}}\\
\Leftrightarrow {x^2} = 49\\
\Leftrightarrow {x^2} = {7^2}\\
\Leftrightarrow x = \pm 7\\
c,\\
{x^4} = - \dfrac{{16}}{{625}}\\
{x^4} \ge 0,\,\,\,\forall x\\
\Rightarrow Phương \,\,\,\,trình \,\,\,\,đã\,\,\,\,cho\,\,\,\,vô\,\,\,\,nghiệm\\
d,\\
{\left( {5 - x} \right)^3} = 343\\
\Leftrightarrow {\left( {5 - x} \right)^3} = {7^3}\\
\Leftrightarrow 5 - x = 7\\
\Leftrightarrow x = 5 - 7\\
\Leftrightarrow x = - 2\\
2,\\
a,\\
\dfrac{{{{\left( { - 5} \right)}^{60}}{{.30}^5}}}{{{{15}^5}{{.5}^{61}}}} = \dfrac{{{5^{60}}.{{\left( {5.2.3} \right)}^5}}}{{{{\left( {3.5} \right)}^5}{{.5}^{61}}}}\\
= \dfrac{{{5^{60}}{{.5}^5}{{.2}^5}{{.3}^5}}}{{{3^5}{{.5}^5}{{.5}^{61}}}} = \dfrac{{{5^{65}}{{.2}^5}{{.3}^5}}}{{{3^5}{{.5}^{66}}}} = \dfrac{{{2^5}}}{5} = \dfrac{{32}}{5}\\
b,\\
{\left( { - \dfrac{1}{3}} \right)^2} - {\left( { - \dfrac{{12}}{{17}}} \right)^0} + {\left( { - \dfrac{1}{2}} \right)^3}{.4^2}\\
= \dfrac{1}{9} - 1 + \dfrac{{ - 1}}{8}.16\\
= - \dfrac{8}{9} - 2 = - \dfrac{{26}}{9}\\
3,\\
a,\\
{7^6} + {7^5} - {7^4} = {7^4}.\left( {{7^2} + 7 - 1} \right) = {7^4}.55\\
55 \vdots 11 \Rightarrow \left( {{7^4}.55} \right) \vdots 11\\
\Rightarrow \left( {{7^6} + {7^5} - {7^4}} \right) \vdots 11\\
b,\\
{10^9} + {10^8} + {10^7} = {10^7}.\left( {{{10}^2} + 10 + 1} \right) = {10^7}.111\\
= {10^6}.10.111 = {10^6}.1110\\
1110 \vdots 222 \Rightarrow \left( {{{10}^6}.1110} \right) \vdots 222\\
\Rightarrow \left( {{{10}^9} + {{10}^8} + {{10}^7}} \right) \vdots 222
\end{array}\)
