Algebra 2 Practice Test: Rational Exponents and nth Roots

Take the cube root first, then square: ³√(27) = 3 and 3² = 9. The answer 18 multiplies 27 by 23 instead.

⁴√(16) = 2 and 2³ = 8; the negative exponent means the reciprocal, so the value is 18. A negative exponent never makes the result negative.

In x^m/n the denominator n is the index of the root and the numerator m is the power: x^3/5 = ⁵√(x³).

When multiplying powers with the same base, add the exponents: 12 + 13 = 56. Multiplying the exponents gives the trap x^1/6.

Apply the exponent to each factor: 8^1/3 = 2 and (x⁶)^1/3 = x². The power must also act on the 8.

Raise both sides to the 23 power: x = 64^2/3 = (³√(64))² = 4² = 16. The answer 512 raises 64 to the 32 power instead.

(−5)³ = −125, so the real cube root is −5. Odd roots of negative numbers are real; only even roots of negatives are not.

32 = 16 · 2 and ⁴√(16) = 2; also ⁴√(x⁸) = x². So the expression is 2x²⁴√(2). Taking half of the exponent 8 gives the wrong x⁴.

Divide by 2: x^3/4 = 27. Raise to the 43 power: x = 27^4/3 = 3⁴ = 81. Check: 81^3/4 = 3³ = 27.

The exponent 12 means a square root, and the negative sign means a reciprocal: x^−1/2 = 1x.