When the space station's energy reactor suddenly shut down, Emek and Luna rushed to the control room before life-support reserves ran low. The emergency display showed several power settings written with exponents, including 2^3 * 2^4 and (3^2)^2. To identify the correct restart sequence, they simplified each expression by applying the rules of exponents and compared the results with the required reactor output. Their calculations revealed the correct configuration, the reactor restarted smoothly, and power returned to every critical system.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
When multiplying powers with the same base, add the exponents.
The reactor display showed the expression 2^3 * 2^4. Which simplified expression is correct?
2^74^72^122^1Correct! 2^3 * 2^4 = 2^(3+4) = 2^7.
Use the exponent rule for multiplying powers with the same base.
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Hint
For a power raised to another power, multiply the exponents first.
The reactor display also showed (3^2)^2. What is the value of this expression?
Correct! (3^2)^2 = 3^(2*2) = 3^4 = 81.
Remember that powers of powers require multiplying the exponents.
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Hint
First simplify both expressions, then compare their values.
The engineers compared the two reactor settings 2^3 * 2^4 and (3^2)^2. Which statement is true?
2^3 * 2^4 is greater because 2^7 = 128Both expressions have the same value(3^2)^2 is greater because 81 is greater than 1282^3 * 2^4 is greater because 128 is greater than 81Correct! 2^3 * 2^4 = 2^7 = 128 and (3^2)^2 = 81, so the first expression is greater.
Calculate each expression before comparing the results.
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