What value of \( n \) solves the equation \( 4^n = \frac{1}{64} \)?

Explain how to find the solution.

4 n = 64 1 ​ 4 n = ( 1 64 ​ ) − 1 4 n = 6 4 − 1 4 n = ( 4 3 ) − 1 4 n = 4 3 ∗ ( − 1 ) 4 n = 4 − 3 = − 3

Answered by Lilith | 2024-06-10

To solve 4 n = 64 1 ​ , we recognize that 64 1 ​ equals 4 − 3 . Therefore, setting the exponents equal gives n = − 3 .
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Answered by Lilith | 2024-12-24