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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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