Calculate (2/6)³: Cube of a Simple Fraction

Question

(26)3= (\frac{2}{6})^3=

Video Solution

Solution Steps

00:04 First, let's simplify this expression.
00:08 We'll break down 6 into factors of 2 and 3.
00:12 Next, we'll reduce any common factors.
00:17 Now, we'll use the formula for fractions with exponents.
00:21 Remember, raising a fraction to a power...
00:25 ...means raising both numerator and denominator.
00:29 Let's apply this formula to our problem.
00:32 Don't forget, both numerator and denominator need exponents.
00:37 Let's carefully calculate these powers.
00:40 And there you have it! That's the solution.

Step-by-Step Solution

We use the formula:

(ab)n=anbn (\frac{a}{b})^n=\frac{a^n}{b^n}

(26)3=(22×3)3 (\frac{2}{6})^3=(\frac{2}{2\times3})^3

We simplify:

(13)3=1333 (\frac{1}{3})^3=\frac{1^3}{3^3}

1×1×13×3×3=127 \frac{1\times1\times1}{3\times3\times3}=\frac{1}{27}

Answer

127 \frac{1}{27}

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