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Exponents and rootsArithmeticHigh schoolabout 0:42

Evaluate 81^(0.25): animated lesson

A narrated, step-by-step exponents and roots video lesson with captions. Final answer: 3.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Evaluate 81^(0.25).
2. Step by step
1. $81^{\frac{1}{4}}$
  Identify the base and exponent
2. $81^{\frac{1}{4}} = \left(\sqrt[4]{81}\right)^{1}$
  Fractional exponent rule
3. $3$
  Take the 4th root exactly
3. The answer
$3$
81^1/4 = 3
4. Check
- Decimal check: 81^0.25 ≈ 3.

Transcript

The problem. Here is the problem: Evaluate 81 to the power 0.25. Raise 81 to the power 1 over 4.

Step by step. Identify the base and exponent. base b equals 81, exponent n equals 1 over 4. Fractional exponent rule. b to the power m/n) equals ( to the power nthe square root of b to the power m: the denominator 4 is the root, the numerator 1 is the power. Take the 4th root exactly.

The answer. So the answer is 3. 81 raised to 1 over 4 equals 3.

Check. Decimal check: 81 to the power 0.25 approximately 3.

About exponents and roots

Evaluate powers, square roots and cube roots, and apply the laws of exponents.

Evaluate 81^(0.25): Exponents and roots Step-by-Step Lesson