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Popular >

simplify (2^4*16^{-2})^3

Solution

simplify

(2^{4} \cdot 1 6^{- 2})^{3}

Solution

\frac{1}{4096}

+1

Decimal Notation

0.00024 \dots

Solution steps

(2^{4} \cdot 1 6^{- 2})^{3}

Apply exponent rule:

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

(2^{4} \cdot 1 6^{- 2})^{3} = (2^{4})^{3} (1 6^{- 2})^{3}

= (2^{4})^{3} (1 6^{- 2})^{3}

(2^{4})^{3} = 4096

= 4096 (1 6^{- 2})^{3}

Apply exponent rule:

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

(1 6^{- 2})^{3} = 1 6^{- 2 \cdot 3}

= 4096 \cdot 1 6^{- 2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= 4096 \cdot 1 6^{- 6}

Apply exponent rule:

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

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

= 4096 \cdot \frac{1}{1 6 ^{6}}

1 6^{6} = 16777216

= 4096 \cdot \frac{1}{16777216}

4096 \cdot \frac{1}{16777216} = \frac{1}{4096}

= \frac{1}{4096}

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Frequently Asked Questions (FAQ)

What is (2^4*16^{-2})^3 ?
The solution to (2^4*16^{-2})^3 is 1/4096