7
QuizMultiple Choice

Solving Exponential Equations by Rewriting the Base — Quiz

Question 7 • Mathematics III

Which equation is equivalent to 16 raised to the 2 p power is equal to 32 raised to the p plus 3 power ?

Answer
A
8 raised to the 4 p power is equal to 8 raised to the 4 p plus 3 power
B
2 raised to the 8 p power is equal to 2 raised to the 5 p plus 3 power
C
2 raised to the 8 p power is equal to 2 raised to the 5 p plus 15 power
D
8 raised to the 4 p power is equal to 8 raised to the 4 p plus 12 power

Explanation

Rewrite each number using a base of 2: 16 = 2⁴ and 32 = 2⁵. Then (2⁴)^(2p) = 2^(8p), while (2⁵)^(p+3) = 2^(5p+15). So the equivalent equation is 2^(8p) = 2^(5p+15), which is choice A.

AI-written and checked against the verified answer.

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