Before activating an experimental gravity gate, Emek and Luna reviewed several calibration formulas on the control screen. The system displayed expressions such as (4^2)^3 and 2^5 * 2^4, each representing a possible energy configuration. They simplified the expressions using exponent rules and checked which result matched the required stability range for the gate. After identifying the correct configuration, they activated the gravity gate and created a safe passage for the waiting spacecraft to travel through.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
For a power raised to another power, multiply the exponents.
The gravity gate displayed the expression (4^2)^3. Which simplified expression is correct?
4^54^616^38^2Correct! (4^2)^3 = 4^(2*3) = 4^6.
Use the rule for powers raised to powers by multiplying the exponents.
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Hint
Add the exponents when multiplying powers with the same base.
The second calibration formula was 2^5 * 2^4. What is the value of this expression?
Correct! 2^5 * 2^4 = 2^(5+4) = 2^9 = 512.
Remember that equal bases allow you to add the exponents.
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Hint
Simplify both expressions before comparing their values.
Emek and Luna compared the two calibration results. Which statement is correct?
(4^2)^3 is greater because 4^6 = 4096Both expressions have the same value2^5 * 2^4 is greater because 512 is greater than 40962^5 * 2^4 is greater because 2^9 is greater than 4^6Correct! (4^2)^3 = 4^6 = 4096, while 2^5 * 2^4 = 2^9 = 512, so the first expression is greater.
Calculate both simplified values and compare them carefully.
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