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Exponents and rootsArithmeticHigh schoolabout 0:44

Evaluate 2/3^(-2): animated lesson

A narrated, step-by-step exponents and roots video lesson with captions. Final answer: 9/4.

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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 2/3^(-2).
2. Step by step
1. $\left(\frac{2}{3}\right)^{-2}$
  Identify the base and exponent
2. $\frac{2}{3}^{-2} = \left(\frac{1}{\frac{2}{3}}\right)^{2}$
  Negative exponent rule
3. $\left(\frac{3}{2}\right) \left(\frac{3}{2}\right) = \frac{9}{4}$
  Multiply the base by itself
3. The answer
$\frac{9}{4}$
2/3^-2 = 9/4
4. Check
- Decimal check: 0.6666666667^-2 ≈ 2.25.

Transcript

The problem. Here is the problem: Evaluate 2 over 3 to the power negative 2. Raise 2 over 3 to the power negative 2.

Step by step. Identify the base and exponent. base b equals 2 over 3, exponent n equals negative 2. Negative exponent rule. A negative exponent means the reciprocal: b^(negative n) equals 1/b to the power n. Multiply the base by itself.

The answer. So the answer is 9 over 4. 2 over 3 raised to negative 2 equals 9 over 4.

Check. Decimal check: 0.6666666667 to the power negative 2 approximately 2.25.

About exponents and roots

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

Evaluate 2/3^(-2): Exponents and roots Step-by-Step Lesson