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5 votes
Rewrite the expression as a power of 1/x²:
a) x⁻²
b) (1/x)²
c) x²
d) (x²)⁻¹

1 Answer

5 votes

Final answer:

All the given expressions
a) x⁻², b) (1/x)², c) x², and d) (x²)⁻¹ can be rewritten as a power of
1/x² by applying the rules for negative exponents and reciprocals.

Step-by-step explanation:

To rewrite the expression as a power of
1/x², we need to convert each of the given expressions accordingly. This involves understanding the rules of exponents particularly regarding negative exponents and how they relate to fractions.

  • a)
    x⁻²: This expression is already the same as
    (1/x²) because a negative exponent indicates the reciprocal. So,
    x⁻² = 1/x².
  • b)
    (1/x)²: Squaring the fraction
    1/x gives us
    (1²)/(x²) which is the same as
    1/x² since
    1² is
    1.
  • c)
    x²: To express
    x² as a power of
    1/x², we take the reciprocal and invert the exponent:
    (x²)⁻¹ = 1/(x²)¹ = 1/x².
  • d)
    (x²)⁻¹: Here, the negative exponent is already present, indicating the reciprocal of
    x², thus (x²)⁻¹ = 1/x².

In conclusion, all the expressions can be rewritten to show the same relationship: they are equal to
1/x² either directly or by applying the exponent rules.

User Martin Cazares
by
7.6k points
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