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Oksi-84 [34.3K]
3 years ago
9

Evaluate: (i) (3/5)^-2(ii) (-3)^-3(iii) (2/7)^-4Need help please.​

Mathematics
2 answers:
zloy xaker [14]3 years ago
5 0

Step-by-step explanation:

# 1

\:   \sf \bigg\lgroup{\dfrac{3}{5}} \bigg\rgroup^{ - 2}

\begin{gathered}\end{gathered}

{\underline{\underline{\sf{\red{Solution :}}}}}

Using the law of exponent :

\dashrightarrow{ \sf{{a}^{ - m}  =  \dfrac{1}{{a}^{m} }}}

\dashrightarrow\:   \sf \bigg\lgroup{\dfrac{3}{5}} \bigg\rgroup^{ - 2}

\dashrightarrow\:   \sf \bigg\lgroup{\dfrac{5}{3}} \bigg\rgroup^{  2}

\dashrightarrow\:   \sf \bigg\lgroup{\dfrac{5}{3} \times \dfrac{5}{3}} \bigg\rgroup

\dashrightarrow\:   \sf \bigg\lgroup{\dfrac{5 \times 5}{3 \times 3}} \bigg\rgroup

\dashrightarrow\:   \sf \bigg\lgroup{\dfrac{25}{9}} \bigg\rgroup

\longrightarrow{\underline{\boxed{\sf{\pink{Answer = \dfrac{25}{9}}}}}}

#2

\sf{\big( - 3 \big)}^{ - 3}

\begin{gathered}\end{gathered}

{\underline{\underline{\sf{\red{Solution :}}}}}

Using the law of exponent :

\dashrightarrow{ \sf{{a}^{ - m}  =  \dfrac{1}{{a}^{m} }}}

\dashrightarrow{\sf{\big( - 3 \big)}^{ - 3} }

\dashrightarrow{\sf{\dfrac{1}{{( - 3)}^{3}}}}

\dashrightarrow{\sf{\dfrac{1}{{( - 3 \times  - 3 \times  - 3)}}}}

\dashrightarrow{\sf{\dfrac{1}{{ - 27}}}}

\longrightarrow{\underline{\boxed{\sf{\pink{Answer = \dfrac{1}{{ - 27}}}}}}}

#3

\: \sf\bigg\lgroup{\dfrac{2}{7}} \bigg\rgroup^{ - 4}

\begin{gathered}\end{gathered}

{\underline{\underline{\sf{\red{Solution :}}}}}

Using the law of exponent :

\dashrightarrow{ \sf{{a}^{ - m}  =  \dfrac{1}{{a}^{m}}}}

\dashrightarrow{\sf{\bigg\lgroup{\dfrac{2}{7}} \bigg\rgroup^{ - 4}}}

\dashrightarrow{\sf{\bigg\lgroup{\dfrac{7}{2}} \bigg\rgroup^{ 4}}}

\dashrightarrow{\sf{\bigg\lgroup{\dfrac{7}{2} \times \dfrac{7}{2} \times \dfrac{7}{2} \times \dfrac{7}{2}} \bigg\rgroup}}

\dashrightarrow{\sf{\bigg\lgroup{\dfrac{7 \times 7 \times 7 \times 7}{2 \times 2 \times 2 \times 2}} \bigg\rgroup}}

\dashrightarrow{\sf{\bigg\lgroup{\dfrac{2401}{16}} \bigg\rgroup}}

\longrightarrow{\underline{\boxed{\sf{\pink{Answer = \dfrac{2401}{16}}}}}}

Xelga [282]3 years ago
3 0
<h3>(I)</h3>

(3/5)⁻² = (5/3)² = 25/9

<h3>(II)</h3>

(-3)⁻³ = (1/-3)³ = 1/-27

<h3>(III)</h3>

(2/7)⁻⁴ = (7/2)⁴ = 2410/16

<u>-</u><u>TheUnknownScientist</u><u> 72</u>

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