Simplify the following:a. $3 \times 10^2$ b. $2^5 \times 5^3$c. $0 \times 10^4$

Given :

The given terms are,

a. $3 \times 10^2$ 

b. $2^5 \times 5^3$

c. $0 \times 10^4$ 

To do :

We have to simplify the given terms and find their value.

Solution :

a. $3 \times 10^2$ 

 $3 \times 10^2 = 3 \times 100 = 300$

Therefore, the value of $3 \times 10^2$ is 300. 

b. $2^5 \times 5^3$

We know that $[a^m \times b^m = (a\times b)^m, a^m \times a^n = (a)^{m+n}]$

$2^5 \times 5^3= 2^2 \times 2^3 \times 5 = 2^2 \times (2\times5)^3 = 4 \times (10)^3 = 4 \times 1000 = 4000$.   

Therefore, the value of $2^5 \times 5^3$ is 4000.

c. $0 \times 10^4$ 

$0 \times 10^4 = 0$.    (Any number multiplied by 0 is 0)

Therefore, the value of $0 \times 10^4$ is 0.

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Updated on: 10-Oct-2022

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