Question

Simplify : (81/625)^-3/4 × [(25/9)^-3/2 + (5/2)^-3]
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Answer 1

Step-by-step explanation:

Given :-

(81/625)^-3/4 × [(25/9)^-3/2 + (5/2)^-3]

To find:-

Simplify the expression?

Solution:-

Given numerical expression is

(81/625)^-3/4 × [(25/9)^-3/2 + (5/2)^-3]

81 = 3×3×3×3 = 3⁴

625=5×5×5×5 = 5⁴

25 = 5×5 = 5²

9 = 3×3 = 3²

Now,

(3⁴/5⁴)^(-3/4) × [ (5²/3²)^(-3/2) + (5/2)^-3]

We know that

(a/b)^m = a^m / b^m

=> [(3/5)⁴]^(-3/4) ×[ {(5/3)²}^(-3/2) + (5/2)^-3]

=>(3/5)^(4×-3/4) ×[(5/3)^(2×-3/2) +(5/2)^-3]

Since (a^m)^n = a^(mn)

=>(3/5)^-3 × [(5/3)^-3 + (5/2)^-3]

We know that a^-n = 1/a^n

=> (5/3)³ ×[(3/5)³+(2/5)³]

=> (125/27) × [ (27/125)+(8/125)]

=> (125/27) ×[(27+8)/125]

=> (125/27)×(35/125)

=> (125×35)/(27×125)

=>(125×35)/(27×125)

=>35/27

Answer:-

The value of the given expression is 35/27

Used formulae:-

• (a/b)^m = a^m / b^m
• (a^m)^n = a^(mn)
• a^-n = 1/a^n

Answer 2

Answer:

35/27

Step-by-step explanation:

☞ (81/625)^-3/4×[(25/9^-3/2+2/5³]

☞ prime factors of 81,625,25 and 9 are as respectively 3⁴,5⁴,5² & 3².

☞ So, (3⁴/5⁴)^(-3/4)×[(5²/3²)^(-3/2)+(2/5)³]

☞ (x/y)^n=x^n/y^n

☞ [(3/5)⁴]^(-3/4)×[{(5/3)²}^(-3/2)+(2/5)³]

☞ (3/5)^(4×-3/4)×[(5/3)^(2×-3/2)+(2/5)³]

☞ Since (x^y)^z = x^(yz)

☞(3/5)^-3 ×[(5/3)^-3 +(2/5)³]

☞as x^-y=1/x^y

☞(5/3)³ ×[(3/5)³+(2/5)³]

☞(125/27) [ (27/125)+(8/125)]

☞(125/27) (27+8)/125]

☞(125/27)x(35/125)

☞(125x35)/(27x125)

☞(125x35)/(27x125)

☞35/27

Equations to remeber!

1.(x/y)^n=x^n/y^n

2.(x^y)^z = x^(yz)

3.x^-y=1/x^y

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