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Exponents and rootsArithmeticHigh schoolabout 0:42

Evaluate 9^(5/2): animated lesson

A narrated, step-by-step exponents and roots video lesson with captions. Final answer: 243.

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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 9^(5/2).
2. Step by step
1. $9^{\frac{5}{2}}$
  Identify the base and exponent
2. $9^{\frac{5}{2}} = \left(\sqrt{9}\right)^{5}$
  Fractional exponent rule
3. $243$
  Take the square root exactly
3. The answer
$243$
9^5/2 = 243
4. Check
- Decimal check: 9^2.5 ≈ 243.

Transcript

The problem. Here is the problem: Evaluate 9 to the power 5 over 2). Raise 9 to the power 5 over 2.

Step by step. Identify the base and exponent. base b equals 9, exponent n equals 5 over 2. Fractional exponent rule. b to the power m/n) equals ( to the power nthe square root of b to the power m: the denominator 2 is the root, the numerator 5 is the power. Take the square root exactly.

The answer. So the answer is 243. 9 raised to 5 over 2 equals 243.

Check. Decimal check: 9 squared.5 approximately 243.

About exponents and roots

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

Evaluate 9^(5/2): Exponents and roots Step-by-Step Lesson