Answer:
[tex]1\, 030\, 224[/tex].
Step-by-step explanation:
Note that multiplying a number by a power of [tex]10[/tex] ([tex]\text{$10$, $100$, $1000$, etc.}[/tex]) is relatively easy in the decimal numeral system:
[tex]1000 \times 1000 = 1\, 000\, 000[/tex].
[tex]30 \times 1000 = 30\, 000[/tex].
To simplify the calculation in this question, make use of the distributive property of multiplication. The goal is to ensure that when multiplications between two large numbers is involved, at least one of the numbers is a power of [tex]10[/tex].
[tex]\begin{aligned} & 1016 \times 1014 \\ =\; & (1000 + 16) \times 1014 \\ =\; & 1000 \times 1014 + 16 \times 1014 \\ =\; & 1000 \times 1014 + 16 \times (1000 + 14) \\ =\; & 1000 \times 1014 + 16 \times 1000 + 16 \times 14 \\ =\; & 1\, 014\, 000 + 16\, 000 + 224 \\ =\; & 1\, 030\, 224\end{aligned}[/tex].
The answer to the expression 10^16 multiplied by 10^14 is 10^30, as exponents are added when multiplying powers of 10 with the same base.
The correct answer to the mathematical expression 1016 imes 1014 is 1030. This is because when you multiply numbers with the same base, you add the exponents. Here, 16 and 14 are added to get 30, leading to the answer of 1030. For the incorrect mathematical expression given as 1016 x 1014, which seems to miss the operations and exponentiation signs, assuming it is meant to represent multiplication of powers of 10 as in the previous example, the operation is the same and the exponents are added together.
Moreover, when performing multiplication in scientific notation, if there are no prefactors other than 1, as in the expression 100 imes 100,000, we add the exponents, so 102 imes 105 = 107.
