Exercise 61

Given that \( x^9 = - 19683 \)   and   \( x^7 = -2187 \), what is the value of \( x \)?

  1. \( 9 \)

  2. \( 3 \)

  3. \( -3 \)

  4. \( 17496 \)

  5. \( -9 \)

Try to solve it before checking the answer.

  1. \( -3 \)

Indeed,

\( x^9 = -19683 = (-3)^9 \)

y

\( x^7 = (-3)^7 \)

Hence:

\[ \boldsymbol{x = -3} \]
\[ x^9 = -19683 = (-3)^9 \quad \text{ y } \quad x^7 = (-3)^7 \]

Hence:   \( \boldsymbol{x = -3} \)

Remark: Just knowing one of the two values is enough: \( x^9 \) ó \( x^7 \).

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