Question

How to do the below sum ?

Answer 1

Given: An expression

To Find - The value of 'x'

Solution:

$(\frac{3}{-2} )^{-3}$ ÷ x = $(\frac{2}{3})^{2}$

• Express with a positive exponent using $(\frac{a}{b})^{-n} = (\frac{b}{a})^{n}$

$(\frac{-2}{3})^{3}$ ÷ x = $(\frac{2}{3})^{2}$

• Dividing is equivalent to multiplying by its reciprocal.

$(\frac{-2}{3})^{3}$ × $\frac{1}{x}$ = $(\frac{2}{3})^{2}$

• Calculate the exponent and accordingly multiply.

$(\frac{-2}{3})^{3}$ × $\frac{1}{x}$ = $(\frac{4}{9})$

• Calculate the exponent and accordingly multiply again.

$-\frac{8}{27}$ × $\frac{1}{x}$ = $(\frac{4}{9})$

• Multiply the fractions.

$-\frac{8}{27x} = \frac{4}{9}$

• Now, cross-multiply.

$-72 = 108x$

• Swap the sides.

$108x = -72$

• Take $108$ to the other side.

$x = \frac{-72}{108}$

• Reduce the fraction

$x = -\frac{2}{3}$

Hence, the value of 'x' is $-\frac{2}{3}$ .