Find the value [(32)^{1{/}5}\times(216)^{-1{/}3}]^{3}

Madhya Pradesh Police Exam Model Paper 5

Question : 98 of 100

Marks: +1, -0

Find the value

[(32)^{1{/}5}×(216)^{-1{/}3}]^{3}

Solution:

Calculation:

[(32)^{1{/}5}×(216)^{-1{/}3}]^{3}

⇒[(2^5)^{1{/}5}×(2^3×3^{}3)^{-1{/}3}]^{3}

⇒[2^1×(2^3)^{-1{/}3}×(3^3)^{-1{/}3}]^{3}

⇒[2^1×2^{-1}×3^{-1}]^3

⇒[2^{1-1}×3^{-1}]^{3}

⇒[2^0×1{/}3]^3

⇒[1×1{/}3]^3

⇒1{/}27

∴[(32)^{1{/}5}×(216)^{-1{/}3}]^3=1{/}27

The correct option is 2 i.e.

1{/}27

a^0=1

a^{-1}=1{/}a

(a^m)^n=a^{mn}

a^m×a^n=a^{m+n}

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