Answer:
[tex]4.16\times 10^{-5}[/tex]
Step-by-step explanation:
Given the expression [tex]\large{\left(5.2\times 10^{-2} \right) \times \left(8.0\times 10^{-4} \right)[/tex], we will use the law of indices to calculate the product of both terms as shown;
Step 1: open the parenthesis
[tex]= \large{\left(5.2\times 10^{-2} \right) \times \left(8.0\times 10^{-4} \right)\\= \large{\left5.2\times 10^{-2} \right \times \left 8.0\times 10^{-4} \right\\[/tex]
Step 2: collect the like terms by bringing the exponentials together
[tex]= \large{\left 5.2\times 8.0 \right \times \left 10^{-2}\times 10^{-4} \right\\[/tex]
step 3: Take the product
[tex]= \large{\left 5.2\times 8.0 \right \times \left 10^{-2}\times 10^{-4} \right\\\\= 41.6 \times 10^{-2-4}\\= 41.6 \times 10^{-6}[/tex]
Step 4: write the final answer in standard form
[tex]= 41.6 \times 10^{-6}\\= 4.16\times 10^{1} \times 10^{-6}\\= 4.16\times 10^{1-6} \\= 4.16\times 10^{-5}[/tex]
Hence the product of the expression in scientific notation is [tex]4.16\times 10^{-5}[/tex]
