Question

Which option is equivalent to the following expression?
$(9.4\times {10}^7)\times (5.8\times {10}^9)$

• A. $545.2\times {10}^9$
• B. $54.52\times {10}^7$
• C. $5.452\times {10}^{10}$
• D. $5.452\times {10}^4$

Answer 1

The correct option is C $5.452\times {10}^{10}$

Given expression is,
$(9.4\times {10}^7)\times (5.8\times {10}^9)$
$=(9.4\times 580)\times ({10}^7\times {10}^9)$
$=\left(5452\right)\times {10}^{7+9}[\because a^m\times a^n=a^{m+n})$]
$=\left(5452\right)\times {10}^{16}$
$=\left(5.452\right)\times {10}^{16}\times {10}^3$
$=\left(5.452\right)\times {10}^{16+3}[\because a^m\times a^n=a^{m+n})$]
$=\left(5.452\right)\times {10}^{19}$