If (√p) 4 = q –2 , and q = – 1 ⁄ 3 , what is one possible value of p?

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Accepted Answer

(√p) 4 = (p 1/2 ) 4 . Multiply the exponents: (p 1/2 ) 4 = p 2 . Substitute – 1 ⁄ 3 for q: p 2 = (– 1 ⁄ 3 ) –2 . A fraction with a negative exponent can be rewritten as the reciprocal of the fraction with a positive exponent: (– 1 ⁄ 3 ) –2 = (–3) 2 = 9. Since p 2 = 9, p = –3 or 3.

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