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3 years ago

Prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1

Mathematics

1 answer:

andreev551 [17]3 years ago

8 0

Answer:

First write them in positive exponent form

(16/81)¾ × [ (9/25)^3/2 ÷ (2/5)³ ]

(2⁴×¾)/ (3⁴×¾) × [ (3² × ^3/2) / (5² ×^3/2) ÷ 2³/5³)

Simplify the terms

2³/3³ × ( 3³ / 5³ ÷ 2³/5³)

Solve the terms in the bracket

2³/3³ × (3³/5³×5³/2³)

You will get

2³/3³ × 3³/2³ = 1

They will cancel each other so the answer will be 1

Hope this helps.

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(This reminds me of a "formula" I developed a few years ago when I was photographing formal groups, and had to figyre out how many people to put in each row, and the rows had to be different lengths) Anyway--

Get the sum of the numbers at the angles, subtract that number from 32, and that's the amount needed for the row.

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AB side: angles given: 8 +4=12 , 32-12 =20 20/2 = 10; 10+1 =11 10-1=9

CD side: angles given: 8 + 12 =20, 32-20=12; 12/2 =6 6+1 =7 6-1 =5

EF side: angles given: 4 + 12 =16 32-16=16 My formula would have yielded 7+9, but those numbers were already used. Conveniently, 10 + 6 are left over. Same principle, but + or - 2.

Thanks for the opportunity to work in this!

It is a fun way for me to end my participation in Brainly for a while. My school year is over!

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Step-by-step explanation:

According to the Question,

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2 years ago

Prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1​

Prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1