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

Question

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

Video Solution

Solution Steps

00:00 Solve
00:03 A power is actually the number multiplied by itself as many times as the exponent
00:06 Make sure to multiply numerator by numerator and denominator by denominator
00:09 Divide by 8
00:12 And this is the solution to the question

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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Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Power of a Quotient

Question Types

Applying Combined Exponents Rules: Factorization Applying Combined Exponents Rules: Binomial Applying Combined Exponents Rules: Applying the formula Applying Combined Exponents Rules: Using multiple rules Powers of a Fraction: Using multiple rules Powers of a Fraction: Applying the formula