Question

$({2}^{89} ) \frac{1}{8}$
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Answer 1

Answer:

$\left(2^{89}\right)\dfrac{1}{8}=2^{86}$

Step-by-step explanation:

$\left(2^{89}\right)\dfrac{1}{8}$

$\gray{\mathrm{Remove\:parentheses}:\quad \left(a\right)=a}$

$=2^{89}\cdot \dfrac{1}{8}$

$\gray{\mathrm{Multiply\:fractions}:\quad \:a\cdot \dfrac{b}{c}=\dfrac{a\:\cdot \:b}{c}}$

$=\dfrac{1\cdot \:2^{89}}{8}$

$\gray{\mathrm{Multiply:}\:1\cdot \:2^{89}=2^{89}}$

$=\dfrac{2^{89}}{8}$

$\gray{\mathrm{Factor}\:8:\quad 2^3}$

$=\dfrac{2^{89}}{2^3}$

$\black{\mathrm{Cancel\:}\dfrac{2^{89}}{2^3}:}$

$\dfrac{2^{89}}{2^3}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \dfrac{x^a}{x^b}=x^{a-b}}$

$\gray{\dfrac{2^{89}}{2^3}=2^{89-3}}$

$=2^{89-3}$

$\gray{\mathrm{Subtract\:the\:numbers:}\:89-3=86}$

$=2^{86}$