Select all the algebraic expressions equivalent to
c²/d².
(cd – 1)²
c²d²
c¹⁰d⁻²/c⁸
(2c2b/4)²
c²d⁻³
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To find the algebraic expressions equivalent to ( frac{c^2}{d^2} ), we can simplify each option:
1. ( (cd – 1)^2 ): Not equivalent, because it expands to ( c^2d^2 – 2cd + 1 ).
2. ( c^2d^2 ): Not equivalent, as it represents ( frac{c^2}{d^2} cdot d^4 ) increasing the degree of ( d ).
3. ( frac{c^{10}d^{-2}}{c^8} ): Simplifies to ( frac{c^{10}}{c^8} cdot d^{-2} = c^{2}d^{-2} = frac{c^2}{d^2} ), so it is equivalent.
4. ( left(frac{2c^2b}{4}right)^2 ): Simplifies to ( left(frac{c^2b}{2}right)^2 = frac{c^4b^2}{4} ), not equivalent.
5. ( c^2d^{-3} ): Not equivalent, as it represents ( frac{c^2}{d^3} ), which is different from ( frac{c^2}{d^2} ).
**Equivalent