Question

4-3 is a power with base 4. which polishing represent it with base 2? a) 2-3 b)-34 c) 26 d)2-6​

Answer 1

Answer:

the answer is 24 I think it is correct

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf{ {4}^{ - 3} \: \: is \: a \: power \: with \: base \: 4}$

which polishing represent it with base 2

$\displaystyle \sf{ a) \: \: {2}^{ - 3} }$

$\displaystyle \sf{ b) \: \: { - 3}^{ 4} }$

$\displaystyle \sf{ c) \: \: {2}^{6} }$

$\displaystyle \sf{ d) \: \: {2}^{ - 6} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\displaystyle \sf{ {( {a}^{m} )}^{ n} = {a}^{mn} }$

EVALUATION

Here the given expression is

$\sf {4}^{ - 3}$

We represent it with base 2 as below

$\sf {4}^{ - 3}$

$\sf = {(4)}^{ - 3}$

$\sf = {(2 \times 2)}^{ - 3}$

$\sf = {( {2}^{2} )}^{ - 3}$

$\sf = { (2)}^{ - 3 \times 2}$

$\sf = { 2}^{ - 6}$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{ d) \: \: {2}^{ - 6} }$

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