The value of

−2
3

−2

3

×

1
3

−4

×
3

−1

×
1
6

is[[1]].

Question

The value of

−2
            3

−2

3
   
   ×

1
        3

−4
   
   ×
    3
    
     −1
   
   ×
    1
    6

is[[1]].

Infinity Learn · Accepted Answer

The value of −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 is 6561 128 .The given expression is −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 .Using the Exponential laws, a b −m = b a m in the given expression −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 −2 2 3 × 3 1 4 × 3 −1 × 1 6 Use, x −m = 1 x m −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 −2 2 3 × 3 1 4 × 1 3 × 1 6 Using law of exponent ( a m ) n = (a) m×n ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 −2 2×3 × 3 1 4 × 1 3 1 × 1 6 ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 −2 6 × 3 1 4 × 1 3 1 × 1 6 ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 −2 6 × 3 4 × 1 3 1 × 1 6 Using law of exponent x y m = x m y m ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 6 (−2) 6 × 3 4 × 1 3 1 × 1 6 ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 6 × 3 4 (−2) 6 × 1 3 1 × 1 6 Using law of exponent x m × x n = x m+n ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 6+4 (−2) 6 × 1 3 1 × 1 3×2 ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 10 (−2) 6 × 1 3 1 × 1 3 1 ×2 ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 1 (−1) 6 × (2) 6 × 1 3 1 × 1 3 1 ×2 Using law of exponent x m × x n = x m+n again, ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 10 1×( 2 6+1 ) × 1 3 1+1 ⇒ −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 = 3 10 2 7 × 1 3 2 Using law of exponent x m x n =x m−n Hence, the correct answer is 6561 128 .

The value of $− 2 3 − 2 3 × 13 − 4 × 3 − 1 × 16$ is[[1]].

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The value of −2 3 −2 3 × 1 3 −4 × 3 −1 × 1 6 is[[1]].

Detailed Solution

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Get Expert Academic Guidance – Connect with a Counselor Today!

The value of $− 2 3 − 2 3 × 13 − 4 × 3 − 1 × 16$ is[[1]].