Question

-4^(-3)×5^(-3)×(〖-5)〗^(-3) Simplify and write the answer in exponential form

Answer 1

SOLUTION

TO DETERMINE

To simplify and write the answer in exponential form

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

FORMULA TO BE IMPLEMENTED

We are aware of the identity on indices that

$\sf{ {a}^{n} \times {b}^{n} = {(ab)}^{n} }$

EVALUATION

Here the given expression is

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

We now simplify it

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

$\sf{ = {( - 4)}^{ - 3} \times {(5 \times - 5)}^{ - 3} } \: ( \: by \: above \: formula)$

$\sf{ = {( - 4)}^{ - 3} \times {( - 25)}^{ - 3} }$

$\sf{ = {( - 4 \times - 25)}^{ - 3} } \: ( \: by \: above \: formula)$

$\sf{ = {100}^{ - 3} }$

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