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

Answers ( )

    0
    2021-09-14T00:36:55+00:00

    Answer:

    Here is your answer:

    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.

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