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Write the answer in proper scientific notation: $\newline$ $(2 \times 10^{5})^{3}$

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Convert between standard and scientific notation

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Q. Write the answer in proper scientific notation:

\newline

(2 \times 10^{5})^{3}

Apply Power Rule: Apply the power of a power rule to the expression $(2x10^{5})^{3}$ . The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . We will apply this rule to both the coefficient $2$ and the base with its exponent $10^{5}$ . $(2^{1})^{3} = 2^{1*3} = 2^{3}$ $(10^{5})^{3} = 10^{5*3} = 10^{15}$
Calculate $2^3$ : Calculate the value of $2^3$ . $\newline$ $2^3 = 2 \times 2 \times 2 = 8$
Combine in Scientific Notation: Combine the results from Step $1$ and Step $2$ to write the expression in scientific notation. $\newline$ We have the coefficient $8$ from Step $2$ and the exponent $15$ from Step $1$ . $\newline$ The scientific notation is $8 \times 10^{15}$ .

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