1.

If $(2000)^{10}$=$1.024\times 10^{k}$., then the value of k is1). 332). 303). 344). 31

Answer»

$(2000)^{10} = 1.024 × 10^k$

$(2^4 × 5^3)^{10} = 1024 × 10^{(k-3)}$

$2^{40} × 5^{30} = 2^{10} × 10^{k-3}$

$2^{10} × 2^{30} × 5^{30} = 2^{10} × 10^{k-3}$

 

$2^30 × 5^30 = 10^{k - 3}$

10^30 = 10^{(k-3)}

 

As the base is same on both SIDES ,

30 = k-3

k = 33



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