Question

Express in power notation
a) – 2401/-256
. b) 1/243

Answer 1

a) -2407   = -7 x -7 x -7 x -7    =  (7/4) ^4
      -256      -4 x -4 x -4 x -4        

b)   1    =  1 x 1x 1 x 1 x 1         = (1/3) ^5
    243      3 x 3 x 3 x 3 x 3

Answer 2

a) $(\frac{7}{4})^{4}$

b) $(\frac{1}{3})^{5}$

Step-by-step explanation:

We have,

a) $\dfrac{-2401}{-256}$

$=\dfrac{2401}{256}$

$=\dfrac{7\times 7\times 7\times 7}{4\times 4\times 4\times 4}$

$=\dfrac{7^{4} }{4^{4} }$

$=(\frac{7}{4})^{4}$

b) $\dfrac{1}{243}$

$=\dfrac{1\times 1\times 1\times 1 \times 1}{3\times 3\times 3\times 3 \times 3}$

$=\dfrac{1^{5} }{3^{5} }$

$=(\frac{1}{3})^{5}$