Why does $9^{3/2}-1^{3/2}$ become 26 in this worked example?

Conditions

• The expression is evaluated exactly using integer powers.
• $9^{3/2} = 27$ and $1^{3/2} = 1$.

Reasoning, step by step

1. Evaluate $9^{3/2}$ by rewriting it as $(\sqrt{9})^3$.
2. Calculate the square root of 9, which is 3.
3. Cube the result: $3^3 = 27$.
4. Evaluate $1^{3/2}$, which is simply 1.
5. Subtract the lower bound value from the upper bound value: $27 - 1 = 26$.

Example

The speaker states, "And then we're going to have 27 minus 1 inside ... So 27 minus 1 is just going to be 26." The board shows the transition from the bracketed expression to $\frac{8}{27}\cdot 26$.

Common misconceptions

• Incorrectly calculating $9^{3/2}$ as $9 \times \frac{3}{2}$ or $9 + \frac{3}{2}$.
• Forgetting that $1$ raised to any power is $1$.
• Making an arithmetic error when subtracting 1 from 27.

Watch the explanation

Explore next

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• How do you multiply $8/27$ by 26 to get the final answer?