Question

find the value of x so that :- (4/5)^-2 /(-4/5)^-2=(1)^3x

Answer 1

The value of x in the given expression is 1

Therefore x=1

Step-by-step explanation:

Given expression is  $\frac{(\frac{4}{5})^{-2}}{(\frac{-4}{5})^{-2}}=(1)^{3x}$

To find the value of x in the given expression :

 $\frac{(\frac{4}{5})^{-2}}{(\frac{-4}{5})^{-2}}=(1)^{3x}$

$\frac{\frac{4^{-2}}{5^{-2}}}{\frac{-4^{-2}}{5^{-2}}}=(1)^{3x}$

$\frac{4^{-2}}{5^{-2}}\times \frac{5^{-2}}{-4^{-2}}=(1)^{3x}$   ( using the properties $a^{-m}=\frac{1}{a^m}}$ and $\frac{1}{a^{-m}}=a^m$ )

$\frac{5^2}{4^2}\times \frac{(-4)^2}{5^2}=(1)^{3x}$ ( using the property $(-a)^2=a^2$ )

$\frac{5^2}{4^2}\times \frac{4^2}{5^2}=(1)^{3x}$

$1=(1)^{3x}$

$(1)^3=(1)^{3x}$

Equating the powers 3=3x

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

Therefore x=1

The value of x in the given expression is 1

Answer 2

Answer:

To find the value of x in the given expression :

\frac{(\frac{4}{5})^{-2}}{(\frac{-4}{5})^{-2}}=(1)^{3x}

(

5

−4

)

−2

(

5

4

)

−2

=(1)

3x

\frac{\frac{4^{-2}}{5^{-2}}}{\frac{-4^{-2}}{5^{-2}}}=(1)^{3x}

5

−2

−4

−2

5

−2

4

−2

=(1)

3x

\frac{4^{-2}}{5^{-2}}\times \frac{5^{-2}}{-4^{-2}}=(1)^{3x}

5

−2

4

−2

×

−4

−2

5

−2

=(1)

3x

( using the properties a^{-m}=\frac{1}{a^m}} and \frac{1}{a^{-m}}=a^m

a

−m

1

=a

m

)

\frac{5^2}{4^2}\times \frac{(-4)^2}{5^2}=(1)^{3x}

4

2

5

2

×

5

2

(−4)

2

=(1)

3x

( using the property (-a)^2=a^2(−a)

2

=a

2

)

\frac{5^2}{4^2}\times \frac{4^2}{5^2}=(1)^{3x}

4

2

5

2

×

5

2

4

2

=(1)

3x

1=(1)^{3x}1=(1)

3x

(1)^3=(1)^{3x}(1)

3

=(1)

3x

Equating the powers 3=3x

x=\frac{3}{3}x=

3

3

Therefore x=1

The value of x in the given expression is 1