Question

step by step explain​

Answer 1

$\sf\huge\bold{Answer:}$

$\fbox{Solution 1}$

Given :

$= ( - 5 ){}^{ - 1}$

To find :

number to be multiplied by

$= ( - 5 ){}^{ - 1}$

to get

$= {(8)}^{ - 1}$

Solution :

$= ( - 5 ){}^{ - 1}$

$⟶ {a}^{ - 1} = \frac{1}{a}$

$= \frac{ \: \: \: \: 1}{ - 5}$

Let the number be x

$\implies \: \frac{ \: \: 1}{ - 5} \times x = {(8)}^{ - 1} \\ \implies \: \frac{ \: \: 1}{ - 5} \times x = \frac{1}{8} \\ \implies \: x = \frac{1}{8} \times - 5 \\ \implies \: x = \frac{ - 5}{8}$

Hence,the number to be multiplied is -5/8.

$\fbox{Solution 2}$

Given :

$= {(3)}^{ - 3}$

To find :

number to be multiplied by

$= {(3)}^{ - 3}$

to get

$= 4$

Solution :

$= {(3)}^{ - 3}$

$⟶ {a}^{ - 1} = \frac{1}{a}$

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

Let the number be x

$\implies \: \frac{1}{ {3}^{3} } \times x = 4 \\ \implies \frac{1}{27 } \times x = 4 \\ \implies \: x = 4 \times 27 \\ \implies \: x = 108$

Hence,the number to be multiplied is 108.

$\fbox{Solution 3}$

Given :

$= {( - 30)}^{ - 1}$

To find :

number to be multiplied by

$= {( - 30)}^{ - 1}$

to get

$= {(6)}^{ - 1}$

Solution :

$= {( - 30)}^{ - 1}$

$⟶ {a}^{ - 1} = \frac{1}{a}$

$= \frac{ \: \: \: 1}{ - 30}$

Let the number be x

$\implies \: \frac{ \: \: 1}{ - 30} \times x = {(6)}^{ - 1} \\ \implies \: \frac{ \: \: 1}{ - 30} \times x = \frac{1}{6} \\ \implies \: x = \frac{1}{6} \times - 30 \\ \implies \: x = - 5$

Hence,the number to be multiplied is -5.

Answer 2

Answer:

Given :

= ( - 5 ){}^{ - 1}=(−5)

−1

To find :

number to be multiplied by

= ( - 5 ){}^{ - 1}=(−5)

−1

to get

= {(8)}^{ - 1}=(8)

−1

Solution :

\begin{gathered} = ( - 5 ){}^{ - 1} \\ \end{gathered}

=(−5)

−1

\begin{gathered}⟶ {a}^{ - 1} = \frac{1}{a} \\ \end{gathered}

⟶a

−1

=

a

1

\begin{gathered}= \frac{ \: \: \: \: 1}{ - 5} \\ \end{gathered}

=

−5

1

Let the number be x

\begin{gathered} \implies \: \frac{ \: \: 1}{ - 5} \times x = {(8)}^{ - 1} \\ \implies \: \frac{ \: \: 1}{ - 5} \times x = \frac{1}{8} \\ \implies \: x = \frac{1}{8} \times - 5 \\ \implies \: x = \frac{ - 5}{8} \end{gathered}

⟹

−5

1

×x=(8)

−1

⟹

−5

1

×x=

8

1

⟹x=

8

1

×−5

⟹x=

8

−5

Hence,the number to be multiplied is -5/8.

\fbox{Solution 2}

Solution 2

Given :

= {(3)}^{ - 3}=(3)

−3

To find :

number to be multiplied by

= {(3)}^{ - 3}=(3)

−3

to get

= 4=4

Solution :

= {(3)}^{ - 3}=(3)

−3

\begin{gathered}⟶ {a}^{ - 1} = \frac{1}{a} \\ \end{gathered}

⟶a

−1

=

a

1

\begin{gathered} = \frac{1}{ {(3)}^{3} } \\ \end{gathered}

=

(3)

3

1

Let the number be x

\begin{gathered}\implies \: \frac{1}{ {3}^{3} } \times x = 4 \\ \implies \frac{1}{27 } \times x = 4 \\ \implies \: x = 4 \times 27 \\ \implies \: x = 108\end{gathered}

⟹

3

3

1

×x=4

⟹

27

1

×x=4

⟹x=4×27

⟹x=108

Hence,the number to be multiplied is 108.

\fbox{Solution 3}

Solution 3

Given :

= {( - 30)}^{ - 1}=(−30)

−1

To find :

number to be multiplied by

= {( - 30)}^{ - 1}=(−30)

−1

to get

= {(6)}^{ - 1}=(6)

−1

Solution :

= {( - 30)}^{ - 1}=(−30)

−1

\begin{gathered}⟶ {a}^{ - 1} = \frac{1}{a} \\ \end{gathered}

⟶a

−1

=

a

1

\begin{gathered} = \frac{ \: \: \: 1}{ - 30} \\ \end{gathered}

=

−30

1

Let the number be x

\begin{gathered}\implies \: \frac{ \: \: 1}{ - 30} \times x = {(6)}^{ - 1} \\ \implies \: \frac{ \: \: 1}{ - 30} \times x = \frac{1}{6} \\ \implies \: x = \frac{1}{6} \times - 30 \\ \implies \: x = - 5\end{gathered}

⟹

−30

1

×x=(6)

−1

⟹

−30

1

×x=

6

1

⟹x=

6

1

×−30

⟹x=−5

Hence,the number to be multiplied is -5.