IM 8.7.5 Lesson: Negative Exponents with Powers of 10

Solve each equation mentally.
[math]\frac{100}{1}=10^x[/math]
[math]\frac{100}{x}=10^1[/math]
[math]\frac{x}{100}=10^0[/math]
[math]\frac{100}{1,000}=10^x[/math]
Complete the table to explore what negative exponents mean.
Match each exponential expression with an equivalent multiplication expression:
Write [math](10^2)^{-3}[/math]as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Match each exponential expression with an equivalent multiplication expression:
Write [math]\frac{10^{-2}}{10^{-5}}[/math] as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Match each exponential expression with an equivalent multiplication expression:
Write [math]10^{-4}\cdot10^3[/math] as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Priya, Jada, Han, and Diego stand in a circle and take turns playing a game.
[size=150]Priya says, SAFE. Jada, standing to Priya's left, says, OUT and leaves the circle. Han is next: he says, SAFE. Then Diego says, OUT and leaves the circle. At this point, only Priya and Han are left. They continue to alternate. Priya says, SAFE. Han says, OUT and leaves the circle. Priya is the only person left, so she is the winner.[br]Priya says, “I knew I’d be the only one left, since I went first.”[/size][br][br]Record this game on paper a few times with different numbers of players. Does the person who starts always win?
Try to find as many numbers as you can where the person who starts always wins. What patterns do you notice?
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– GeoGebra Classroom Activities, IM 6 – 8 Math

Information: IM 8.7.5 Lesson: Negative Exponents with Powers of 10