Question

Evaluate:
(i) (3/5)^-2
(ii) (-3)^-3
(iii) (2/7)^-4

Need help please.​

Answer 1

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 :

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

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

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

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

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

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

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

Answer 2

(I)

(3/5)⁻² = (5/3)² = 25/9

(II)

(-3)⁻³ = (1/-3)³ = 1/-27

(III)

(2/7)⁻⁴ = (7/2)⁴ = 2410/16

-TheUnknownScientist 72