Question

Viết các biểu thức sau dưới dạng một lũy thừa:

6;  3/2 x 9/4 x 81/16

7; (1/2)^7 x 8 x 32 x 2^8

8;  (-1/7)^4 x 125 x 5

9;  4 x 32 : (2^3 x 1/16)

10;  (1/7)^2 x 1/7 x 49

Answer 1

\(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^7\)

\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8=\left(\dfrac{1}{7}\right)^7\times2^{16}\)

\(\left(-\dfrac{1}{7}\right)^4\times125\times5=\left(-\dfrac{1}{7}\right)^4\times5^3\times5=\left(-\dfrac{1}{7}\right)^4\times5^4\)

\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:2^3:2^{-4}=2^0\)

\(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^3\times7^3=1^3\)
 

Answer 2

6, \(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4\)

7,\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8\)

8,\(\left(-\dfrac{1}{7}\right) ^4\times125\times5=\left(\dfrac{1}{7}\right)^4\times5^3\times5\)

9,\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:\left[2^3\times\left(\dfrac{1}{2}\right)^4\right]\)

10, \(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times7^2\)

Answer 3

6) \(...=\dfrac{3}{2}.\left(\dfrac{3}{2}\right)^2.\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^7\)

7) \(...=2^{-7}.2^3.2^5.2^8=2^9\)

8) \(...=\left(\dfrac{1}{7}\right)^4.5^3.5=\left(\dfrac{1}{7}\right)^4.5^4\)

9) \(...=2^2.2^5:\left(2^3.2^{-4}\right)=2^8\)

10) \(...=\left(\dfrac{1}{7}\right)^3.\left(\dfrac{1}{7}\right)^2=\left(\dfrac{1}{7}\right)^5\)

Answer 4

10)...\(...=7^{-3}.7^2=7^{-1}=\dfrac{1}{7}\)

Answer 5

6, \(\dfrac{3}{2}\) \(\times\) \(\dfrac{9}{4}\) \(\times\) \(\dfrac{81}{16}\)

= \(\dfrac{3.3^2.3^4}{2.2^2.2^4}\) 

= \(\dfrac{3^7}{2^7}\)

= (\(\dfrac{3}{2}\))⁷

7;  (\(\dfrac{1}{2}\))⁷ \(\times\) 8 \(\times\)32 \(\times\) 2\(^8\)

= \(\dfrac{1}{2^7}\) \(\times\) 2³ \(\times\) 2⁵ \(\times\) 2⁸

= \(\dfrac{1}{2^7}\) \(\times\) 2¹⁶

= 2⁹

8, (-\(\dfrac{1}{7}\))⁴ \(\times\) 125 \(\times\) 5

= \(\dfrac{1}{7^4}\) \(\times\) 5³ \(\times\) 5

= \(\dfrac{1}{7^4}\) \(\times\) 5⁴

= (\(\dfrac{5}{7}\))⁴

9; 4 \(\times\) 32 : (2³ \(\times\) \(\dfrac{1}{16}\))

= 2² \(\times\) 2⁵ : \(\dfrac{1}{2}\)

= 2² \(\times\) 2⁵ \(\times\) 2

= 2⁸

10;  ( \(\dfrac{1}{7}\))² \(\times\) \(\dfrac{1}{7}\) \(\times\) 49

       = \(\dfrac{1}{7^2}\) \(\times\)7² \(\times\) \(\dfrac{1}{7}\)

       = \(\dfrac{1}{7}\)

        = 7^-1