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Popular >

simplify (2^2)(2^3)(6^{-3})

Solution

simplify

(2^{2}) (2^{3}) (6^{- 3})

Solution

\frac{4}{27}

+1

Decimal Notation

0.14814 \dots

Solution steps

(2^{2}) (2^{3}) (6^{- 3})

(2^{2}) (2^{3}) (6^{- 3}) = 2^{2} \cdot 2^{3} \cdot 6^{- 3}

= 2^{2} \cdot 2^{3} \cdot 6^{- 3}

2^{2} \cdot 2^{3} = 32

= 32 \cdot 6^{- 3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

6^{- 3} = \frac{1}{6 ^{3}}

= 32 \cdot \frac{1}{6 ^{3}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 32}{6 ^{3}}

Multiply the numbers:

1 \cdot 32 = 32

= \frac{32}{6 ^{3}}

Factor

32 : 2^{5}

Factor

6^{3} : 2^{3} \cdot 3^{3}

= \frac{2 ^{5}}{2 ^{3} \cdot 3 ^{3}}

Cancel

\frac{2 ^{5}}{2 ^{3} \cdot 3 ^{3}} : \frac{2 ^{2}}{3 ^{3}}

= \frac{2 ^{2}}{3 ^{3}}

2^{2} = 4

= \frac{4}{3 ^{3}}

3^{3} = 27

= \frac{4}{27}

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Frequently Asked Questions (FAQ)

What is (2^2)(2^3)(6^{-3}) ?
The solution to (2^2)(2^3)(6^{-3}) is 4/27