Question

Value of 4^3/2×(125)^ - 2/3​

Answer 1

Answer:

4^(3/2) × 125^(-2/3) = 8/25 or -8/25

Step-by-step explanation:

We know that,

a^(-m) = 1/(a^m)

a^(m/n) = (nth√a)^m

(a^m)^n = a^(m × n)

also,

If x² = y

x = +√y or -√y

Now,

Case 1

4^(3/2) × 125^(-2/3)

= (√4)³ × (125^(-1))^(2/3)

= 2³ × (1/125)^(2/3)

= 8 × ((³√1)/(³√125))²

= 8 × (1/5)²

= 8 × (1²/5²)

= 8 × (1/25)

= 8/25

Case 2

(√4³) × (125)^(-2/3)

= (√4)³ × (125^(-1))^(2/3)

= (-2)³ × (1/125)^(2/3)

= -8 × ((³√1)/(³√125))²

= -8 × (1/5)²

= -8 × (1²/5²)

= -8 × (1/25)

= -8/25

Thus,

4^(3/2) × 125^(-2/3) = 8/25 or -8/25

Hope it helped and you understood it........All the best

Answer 2

Answer:

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