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Exponents and rootsArithmeticHigh schoolabout 0:54

Evaluate 32^(-3/5): animated lesson

A narrated, step-by-step exponents and roots video lesson with captions. Final answer: ≈ 0.125.

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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 32^(-3/5).
2. Step by step
1. $32^{-\frac{3}{5}}$
  Identify the base and exponent
2. $32^{-\frac{3}{5}} = \left(\frac{1}{32}\right)^{\frac{3}{5}}$
  Negative exponent rule
3. $\frac{1}{32}^{\frac{3}{5}} = \left(\sqrt[5]{\frac{1}{32}}\right)^{3}$
  Fractional exponent rule
3. The answer
$\approx 0.125$
32^-3/5 = ≈ 0.125
4. Check
- Decimal check: 32^-0.6 ≈ 0.125.

Transcript

The problem. Here is the problem: Evaluate 32 to the power negative 3 over 5). Raise 32 to the power negative 3 over 5.

Step by step. Identify the base and exponent. base b equals 32, exponent n equals negative 3 over 5. Negative exponent rule. A negative exponent means the reciprocal: b^(negative n) equals 1/b to the power n. Fractional exponent rule. b to the power m/n) equals ( to the power nthe square root of b to the power m: the denominator 5 is the root, the numerator 3 is the power.

The answer. So the answer is approximately 0.125. The value is approximately 0.125.

Check. Decimal check: 32 to the power negative 0.6 approximately 0.125.

About exponents and roots

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

Evaluate 32^(-3/5): Exponents and roots Step-by-Step Lesson