Question

Calculate the product below and give your answer in scientific notation. \large{\left(5.2\times 10^{-2} \right) \times \left(8.0\times 10^{-4} \right) =\ ?}(5.2×10 −2 )×(8.0×10 −4 )= ?Left parenthesis, 5, point, 2, times, 10, start superscript, minus, 2, end superscript, right parenthesis, times, left parenthesis, 8, point, 0, times, 10, start superscript, minus, 4, end superscript, right parenthesis, equals, space, question mark

Answer 1

Answer:

$4.16\times 10^{-5}$

Step-by-step explanation:

Given the expression $\large{\left(5.2\times 10^{-2} \right) \times \left(8.0\times 10^{-4} \right)$, we will use the law of indices to calculate the product of both terms as shown;

Step 1: open the parenthesis

$= \large{\left(5.2\times 10^{-2} \right) \times \left(8.0\times 10^{-4} \right)\\= \large{\left5.2\times 10^{-2} \right \times \left 8.0\times 10^{-4} \right$

Step 2: collect the like terms by bringing the exponentials together

$= \large{\left 5.2\times 8.0 \right \times \left 10^{-2}\times 10^{-4} \right$

step 3: Take the product

$= \large{\left 5.2\times 8.0 \right \times \left 10^{-2}\times 10^{-4} \right\\\\= 41.6 \times 10^{-2-4}\\= 41.6 \times 10^{-6}$

Step 4: write the final answer in standard form

$= 41.6 \times 10^{-6}\\= 4.16\times 10^{1} \times 10^{-6}\\= 4.16\times 10^{1-6} \\= 4.16\times 10^{-5}$

Hence the product of the expression in scientific notation is $4.16\times 10^{-5}$