What is (2^5*(2^3)^4)/(2^{13)} ?

The solution to (2^5*(2^3)^4)/(2^{13)} is 16

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simplify (2^5*(2^3)^4)/(2^{13)}

simplify

\frac{2 ^{5} \cdot ( 2 ^{3} ) ^{4}}{2 ^{13}}

16

Solution steps

\frac{2 ^{5} ( 2 ^{3} ) ^{4}}{2 ^{13}}

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

= \frac{2 ^{5} \cdot 4096}{2 ^{13}}

\frac{2 ^{5}}{2 ^{13}} = \frac{1}{2 ^{8}}

= \frac{4096}{2 ^{8}}

Factor the number:

4096 = 2^{12}

= \frac{2 ^{12}}{2 ^{8}}

Apply exponent rule:

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

= 2^{12 - 8}

Subtract the numbers:

12 - 8 = 4

= 2^{4}

2^{4} = 16

= 16

(3 x + 2 a) (3 x - 5 a)

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