What is ((4^8)^2*64)/(4^{20)} ?

The solution to ((4^8)^2*64)/(4^{20)} is 1/4

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simplify ((4^8)^2*64)/(4^{20)}

simplify

\frac{( 4 ^{8} ) ^{2} \cdot 64}{4 ^{20}}

\frac{1}{4}

Solution steps

\frac{( 4 ^{8} ) ^{2} \cdot 64}{4 ^{20}}

(4^{8})^{2} = 4^{16}

= \frac{4 ^{16} \cdot 64}{4 ^{20}}

\frac{4 ^{16}}{4 ^{20}} = \frac{1}{4 ^{4}}

= \frac{64}{4 ^{4}}

Factor the number:

64 = 4^{3}

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

Apply exponent rule:

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

= \frac{1}{4 ^{4 - 3}}

Subtract the numbers:

4 - 3 = 1

= \frac{1}{4 ^{1}}

Apply exponent rule:

a^{1} = a

4^{1} = 4

= \frac{1}{4}

x \cdot (2 x)^{2}

\frac{2 + 3}{2 - 3}

lo g_{10} (7) - lo g_{10} (3) + lo g_{10} (6)

\frac{8}{x ^{2} + 6 x} \cdot 2 x

- \frac{2}{3} \cdot (- 1)