What is (6*6^{-6})^5 ?

The solution to (6*6^{-6})^5 is 1/(3^{25)*33554432}

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simplify (6*6^{-6})^5

simplify

(6 \cdot 6^{- 6})^{5}

\frac{1}{3 ^{25} \cdot 33554432}

Solution steps

(6 \cdot 6^{- 6})^{5}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(6 \cdot 6^{- 6})^{5} = 6^{5} (6^{- 6})^{5}

= 6^{5} (6^{- 6})^{5}

6^{5} = 7776

= 7776 (6^{- 6})^{5}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(6^{- 6})^{5} = 6^{- 6 \cdot 5}

= 7776 \cdot 6^{- 6 \cdot 5}

Multiply the numbers:

6 \cdot 5 = 30

= 7776 \cdot 6^{- 30}

Apply exponent rule:

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

6^{- 30} = \frac{1}{6 ^{30}}

= 7776 \cdot \frac{1}{6 ^{30}}

Multiply fractions:

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

= \frac{1 \cdot 7776}{6 ^{30}}

Multiply the numbers:

1 \cdot 7776 = 7776

= \frac{7776}{6 ^{30}}

Factor

7776 : 2^{5} \cdot 3^{5}

Factor

6^{30} : 2^{30} \cdot 3^{30}

= \frac{2 ^{5} \cdot 3 ^{5}}{2 ^{30} \cdot 3 ^{30}}

Cancel

\frac{2 ^{5} \cdot 3 ^{5}}{2 ^{30} \cdot 3 ^{30}} : \frac{1}{2 ^{25} \cdot 3 ^{25}}

= \frac{1}{2 ^{25} \cdot 3 ^{25}}

2^{25} = 33554432

= \frac{1}{3 ^{25} \cdot 33554432}

6^{3} \cdot 6^{5}

16 m^{2} - 9 n^{2}

\frac{3}{26}

8 x^{5}