Question

can anyone give me the explanation

how to solve this ??​

Answer 1

Answer:

this is questions of algebraic expression

Step-by-step explanation:

first you have to reciprocal then -2 become to 2 then do 3×3 and the answe is 9/25

5×5

this is the answer of i

Answer 2

Answer:

1. Evaluate :

${\underline{\underline{\sf{\red{Question :}}}}}$

$\dashrightarrow(i) \: \sf \bigg\lgroup{\dfrac{3}{5}} \bigg\rgroup^{ - 2}$

$\begin{gathered}\end{gathered}$

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

Using the law of exponent :

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

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

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

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

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

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

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

∴ The answer is 25/9.

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${\underline{\underline{\sf{\red{Question :}}}}}$

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

$\begin{gathered}\end{gathered}$

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

Using the law of exponent :

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

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

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

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

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

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

∴ The answer is 1/-27.

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${\underline{\underline{\sf{\red{Question :}}}}}$

$\dashrightarrow(i) \: \sf\bigg\lgroup{\dfrac{2}{7}} \bigg\rgroup^{ - 4}$

$\begin{gathered}\end{gathered}$

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

Using the law of exponent :

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

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

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

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

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

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

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

∴ The answer is 2401/16.

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Learn More :

${\underline{\underline{\sf{\red{Exponent :}}}}}$

The exponent of a number says how many times to use the number in a multiplication.

$\begin{gathered}\end{gathered}$

${\underline{\underline{\sf{\red{Rule \: of \: exponent :}}}}}$

The important laws of exponents are given below:

$\dashrightarrow{\sf{{a}^{m} \times {a}^{n} = {a}^{m + n}}}$

$\dashrightarrow{\sf{{a}^{m}/{a}^{n} = {a}^{m - n}}}$

$\dashrightarrow{\sf{({a}^{m})^{n} = {a}^{mn} }}$

$\dashrightarrow{\sf{{a}^{n}/{b}^{n} = ({a/b})^{n} }}$

$\dashrightarrow{\sf{{a}^{0} = 1}}$

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

$\dashrightarrow{ \sf{{a}^{\frac{1}{n} } = \sqrt[n]{a}}}$

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