Write the answer in proper scientific notation: (100 x10^(6))^(4)

Simplify Base: Simplify the base of the expression before applying the exponent. We have the expression (100 x 10^6). The number 100 can be written as 10^2, so we can rewrite the expression as (10^2 x 10^6).Combine Bases: Apply the laws of exponents to combine the bases. When multiplying with the same base, we add the exponents: 10^2 x 10^6 = 10^(2+6) = 10^8.Power of Power Rule: Apply the power of a power rule. Now we have (10^8)^4. According to the power of a power rule, we multiply the exponents: (10^8)^4 = 10^(8*4) = 10^32.Final Answer: Write the final answer in scientific notation. The expression is already in scientific notation, so the final answer is 10^32.

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Write the answer in proper scientific notation: $\newline$ $(100 \times 10^{6})^{4}$

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Math Problems

Grade 8

Convert between standard and scientific notation

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Q. Write the answer in proper scientific notation:

\newline

(100 \times 10^{6})^{4}

Simplify Base: Simplify the base of the expression before applying the exponent. $\newline$ We have the expression $(100 \times 10^6)$ . The number $100$ can be written as $10^2$ , so we can rewrite the expression as $(10^2 \times 10^6)$ .
Combine Bases: Apply the laws of exponents to combine the bases. $\newline$ When multiplying with the same base, we add the exponents: $10^2 \times 10^6 = 10^{(2+6)} = 10^8$ .
Power of Power Rule: Apply the power of a power rule. $\newline$ Now we have $(10^8)^4$ . According to the power of a power rule, we multiply the exponents: $(10^8)^4 = 10^{8*4} = 10^{32}$ .
Final Answer: Write the final answer in scientific notation. $\newline$ The expression is already in scientific notation, so the final answer is $10^{32}$ .