If x = 5/8^-2 × 12/15^-2, then the value of x^-3 is
Answers
Answer:
1/64
Step-by-step explanation:
Here is your answer:
Given that,
x = (\frac{5}{8})^{-2} ( \frac{12}{15})^{-2}x=(
8
5
)
−2
(
15
12
)
−2
To find,
The\ value\ of \ x^{-3}The value of x
−3
Solution:
We know that,
a^{-n}= (\frac{1}{a})^{n}a
−n
=(
a
1
)
n
--- (Identity)
Then,
x = (\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 = \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} = \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.