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Exponents and rootsArithmeticHigh schoolabout 0:45

Evaluate 27^(4/3): animated lesson

A narrated, step-by-step exponents and roots video lesson with captions. Final answer: 81.

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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 27^(4/3).
2. Step by step
1. $27^{\frac{4}{3}}$
  Identify the base and exponent
2. $27^{\frac{4}{3}} = \left(\sqrt[3]{27}\right)^{4}$
  Fractional exponent rule
3. $81$
  Take the cube root exactly
3. The answer
$81$
27^4/3 = 81
4. Check
- Decimal check: 27^1.333333333 ≈ 81.

Transcript

The problem. Here is the problem: Evaluate 27 to the power 4 over 3). Raise 27 to the power 4 over 3.

Step by step. Identify the base and exponent. base b equals 27, exponent n equals 4 over 3. Fractional exponent rule. b to the power m/n) equals ( to the power nthe square root of b to the power m: the denominator 3 is the root, the numerator 4 is the power. Take the cube root exactly.

The answer. So the answer is 81. 27 raised to 4 over 3 equals 81.

Check. Decimal check: 27 to the power 1.333333333 approximately 81.

About exponents and roots

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

Evaluate 27^(4/3): Exponents and roots Step-by-Step Lesson