Geoffrey is evaluating the expression (-3)^6(2^6)/(-3)^5(2^2) as shown below.

Mathematics

1 answer:

Alekssandra [29.7K]2 years ago

3 0

Answer:

48.

Step-by-step explanation:

First you multiply the number by itself as many times as the number of the exponent is. In this case you multiply -3 to itself 6 times which makes -729, 2 to the 6th power is 64, -3 to the 5th power is -243, and 2 to the 2nd power is 4. Then you multiply -729 by 64 which makes -46656 and multiply -243 by 4 which makes -972, and then divide -972 from -46656 which makes 48.

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$\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
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$\bf \pm\sqrt{13^2-5^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a \implies \stackrel{II~quadrant}{-12=a}
\\\\\\
therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}
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