After a software update, a deep-space communication array began producing conflicting signal calculations, threatening contact with an exploration probe. Emek and Luna examined several transmission settings written with exponents, including 5^2 * 5^3 and 10^6 / 10^2. They simplified each expression using the rules of exponents, compared the resulting outputs, and matched them to the required signal strength. Their careful analysis restored the correct transmission settings, and communication with the probe continued without interruption.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
When multiplying powers with the same base, add the exponents.
The communication array used the expression 5^2 * 5^3. Which simplified form is correct?
5^510^55^625^3Correct! 5^2 * 5^3 = 5^(2+3) = 5^5.
Check the exponent rule for multiplying powers with the same base.
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Hint
When dividing powers with the same base, subtract the exponents.
The array also used the expression 10^6 / 10^2. What is the value of this expression?
Correct! 10^6 / 10^2 = 10^(6-2) = 10^4 = 10000.
Remember to subtract the denominator exponent from the numerator exponent.
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Hint
Simplify each expression first, then compare the two numbers.
The engineers compared the two signal settings. Which statement is correct after simplifying both expressions?
5^2 * 5^3 is greater because 5^5 = 3125Both expressions have the same value10^6 / 10^2 is greater because 10000 is greater than 31255^2 * 5^3 is greater because 3125 is greater than 10000Correct! 5^2 * 5^3 = 3125 and 10^6 / 10^2 = 10000, so the second expression is greater.
Calculate both simplified values before comparing them.
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