## 4. If x=(5/8)¯² (12/15)¯² then what is value of x-3 ​

Question

4. If x=(5/8)¯² (12/15)¯²
then what is value of x-3

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2 weeks 2021-09-14T00:35:25+00:00 1 Answer 0 views 0

Given that,

x=(58)−2(1215)−2x = (\frac{5}{8})^{-2} ( \frac{12}{15})^{-2}x=(

8

5

)

−2

(

15

12

)

−2

To find,

The value of x−3The\ value\ of \ x^{-3}The value of x

−3

Solution:

We know that,

a−n=(1a)na^{-n}= (\frac{1}{a})^{n}a

−n

=(

a

1

)

n

— (Identity)

Then,

x=(58)−2×(1215)−2=(85)2×(1512)2x = (\frac{5}{8})^{-2} \times ( \frac{12}{15})^{-2} = ( \frac{8}{5})^{2} \times ( \frac{15}{12})^{2}x=(

8

5

)

−2

×(

15

12

)

−2

=(

5

8

)

2

×(

12

15

)

2

⇒ x=8×85×5×15×1512×12=2×21×1×3×33×3=2×2=4x = \frac{8\times 8}{5\times 5} \times \frac{15\times 15}{12\times 12} = \frac{2\times 2}{1\times 1} \times \frac{3\times 3}{3\times 3} = 2\times 2 = 4x=

5×5

8×8

×

12×12

15×15

=

1×1

2×2

×

3×3

3×3

=2×2=4

So , x = 4

Then,

x−3=1×3=143=14×4×4=164x^{-3} = \frac{1}{x^{3}} = \frac{1}{4^{3}} = \frac{1}{4\times 4\times 4} = \frac{1}{64}x

−3

=

x

3

1

=

4

3

1

=

4×4×4

1

=

64

1

Therefore the answer is 1 / 64.