Question

Simplify and express the result in positive powers: (4-^3 ÷ 4 -^5 ) x 4 -^7​

Answer 1

So we need to simplify :

$( {4}^{ - 3} \div {4}^{ - 5} ) \times {4}^{ - 7}$

Now,

We know :

${a}^{m} \div {b}^{n} = {a}^{(m - n)}$

and

${a}^{m} \times {a}^{n} = {a}^{(m + n)}$

Applying these two conditions we get :

$( {4}^{(- 3) - ( - 5)} ) \times {4}^{ - 7}$

$( {4}^{( - 3 + 5)} ) \times {4}^{ - 7}$

$( {4}^{2} ) \times 4 {}^{ - 7}$

${4}^{(2 + ( - 7))}$

${4}^{(2 - 7)}$

${4}^{ - 5}$

Now, we need to convert it into positive power :

thus,

${ {4}^{ - 5} }$ = $\frac{1}{ {4}^{5} }$

THUS, your answer is :

$\frac{1}{ {4}^{5} }$

HOPE THIS HELPS

THANKS

Answer 2

Answer:

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