Giải Bài 4 trang 25

Đề bài

Viết kết quả mỗi phép tính sau dưới dạng một lũy thừa:

a) $3^4{.3}^5$;     ${16.2}^9$;    $16.32$;

b) ${12}^8:12$;  $243:3^4$;  ${10}^9:10000$.

c) ${4.8}^6.2{.8}^3$;  ${12}^2.2{.12}^3.6$;  $6^3.2{.6}^4.3$.

Lời giải chi tiết

a)

Ta có: $3^4{.3}^5=3^{4+5}=3^9$;     

Ta có: $16=\mathrm{2.2.2.2}=2^4$.

$\Rightarrow$ ${16.2}^9=2^4{.2}^9=2^{4+9}=2^{13}$; 

Ta có: $32=\mathrm{2.2.2.2.2}=2^5$

$\Rightarrow$ $16.32=2^4{.2}^5=2^{4+5}=2^9$

b)

${12}^8:12={12}^8:{12}^1={12}^{8-1}={12}^7$;

Ta có: $243=\mathrm{3.3.3.3.3}=3^5$

$\Rightarrow 243:3^4=3^5:3^4=3^{5-4}=3^1=3$.

Ta có: $10000={10}^4$

$\Rightarrow$${10}^9:10000={10}^9:{10}^4={10}^{9-4}={10}^5$

c)

$\begin{array}{c}{4.8}^6.2{.8}^3={\mathrm{4.2.8}}^6{.8}^3\\ =\left(4.2\right){.8}^6{.8}^3\\ ={8.8}^6{.8}^3\\ =8^1{.8}^6{.8}^3\\ =8^{1+6+3}=8^{10}\end{array}$

$\begin{array}{c}{12}^2.2{.12}^3.6\\ ={12}^2{.12}^3.\left(2.6\right)\\ ={12}^2{.12}^3.12\\ ={12}^{2+3+1}={12}^6\end{array}$

$\begin{array}{c}{6}^3.2{.6}^4.3\\ =6^3{.6}^4.\left(2.3\right)\\ =6^3{.6}^4.6\\ =6^{3+4+1}\\ =6^8\end{array}$

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