Question

(3/2)^-1 ÷ (-2/5)^-1​

Answer 1

To Solve:-

$\red{➤}\:$$\sf ({\frac{3}{2}})^{-1}÷ ({\frac{-2}{5}})^{-1}$

Solution:-

Since the power is in negetive,we write the reciprocal of the number and then solve it like positive exponents-

$\begin{gathered}\\\quad\longrightarrow\quad\sf( {\dfrac{3}{2}})^{-1}÷ ({\dfrac{-2}{5}})^{-1}\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf ({\dfrac{2}{3}})^{1}÷ ({\dfrac{5}{-2}})^{1}\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf \dfrac{2}{3}÷ \dfrac{5}{(-2)}\quad (a^1=a)\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf \dfrac{2}{3}×\dfrac{(-2)}{5}\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf \dfrac{2×(-2)}{3×5}\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\boxed{\sf{ \dfrac{-4}{15}}}\\\end{gathered}$

Know More-

Laws of Exponents-

$\sf a^m×a^n = a^{m+n}$

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

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

$\sf a^n/b^n = (a/b)^n$

$\sf a^0 = 1$

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

Answer 2

Answer:

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Step-by-step explanation:

-4/15 ≅ -0.2666667

Exponentiation: 3/2 ^ (-1) = 21/31 = 2/3

In words - three halfs raised to the power of to minus one = two thirds.

Exponentiation: (-2/5) ^ (-1) = 51/-21 = 5/-2 = -5/2

In words - minus two fifths raised to the power of to minus one = minus five halfs.

Divide: the result of step No. 1 : the result of step No. 2 = 2/3 : (-5/2) = 2/3 · -2/5 = 2 · (-2)/3 · 5 = -4/15

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of -5/2 is 2/-5) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - two thirds divided by minus five halfs = minus four fifteenths.