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Negative Exponents quiz

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  • What does a negative exponent indicate in an expression like a^-n?
    A negative exponent indicates the reciprocal of the base raised to the positive exponent; a^-n = 1/a^n.
  • How do you rewrite 2^-3 with a positive exponent?
    2^-3 can be rewritten as 1/(2^3).
  • What is the result of simplifying 6^-2?
    6^-2 simplifies to 1/(6^2), which is 1/36.
  • If you have a negative exponent in the numerator, what should you do?
    Flip the expression to the denominator and change the exponent to positive.
  • How do you handle a negative exponent in the denominator, such as 1/x^-3?
    Move the base with the negative exponent to the numerator and make the exponent positive, so 1/x^-3 = x^3.
  • What is the general rule for converting a negative exponent to a positive exponent?
    Write the reciprocal of the base and change the exponent to positive.
  • How can you express any expression as a fraction to apply the negative exponent rule?
    You can divide the expression by 1 to make it a fraction.
  • What happens to the exponent when you move a base from the numerator to the denominator?
    The exponent changes sign; a^-n in the numerator becomes a^n in the denominator.
  • What is the simplified form of (2^2)/(2^5)?
    (2^2)/(2^5) simplifies to 2^-3, which is 1/(2^3).
  • Why is there an 'invisible one' in the numerator after canceling all terms?
    When all terms in the numerator are canceled, a 1 remains because any number divided by itself is 1.
  • What does it mean to 'flip' an expression when dealing with negative exponents?
    Flipping means writing the reciprocal of the base and changing the exponent to positive.
  • If you have x^-4 in the denominator, how do you rewrite it?
    Move x^-4 to the numerator and write it as x^4.
  • What is the simplified form of 1/(y^-2)?
    1/(y^-2) simplifies to y^2.
  • How do you simplify an expression like a^-1?
    a^-1 simplifies to 1/a.
  • Why is mastering negative exponents important in algebra?
    It helps in simplifying exponential expressions, manipulating polynomials, and understanding the quotient of powers.