MHB How this exponent expression is reduced

AI Thread Summary
The expression A initially contains 8 terms but is reduced to 5 through simplification. The term -10^22 is rewritten as -10×10^21, allowing for the combination with 12×10^21 to yield 2×10^21. Similarly, -12×10^15 and 61×10^14 are combined to produce -59×10^14. The terms 3×10^9 and -36×10^8 are also simplified to -60×10^7. This process demonstrates how combining like terms effectively reduces the expression.
Sabeel
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Initially the expression A has 8 terms. So how is it reduced in the second line to 5 terms?
Could you show me, please?
Thank you.
\begin{align*}
A&=10^{28} -10^{22} +61\times10^{14}+12\times10^{21}-12\times10^{15}+3\times10^{9}-36\times10^{8}+9\times10^{2}\\
&=10^{28} +2\times10^{21}-59\times10^{14}-60\times10^{7}+9\times10^{2}
\end{align*}
 
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Sabeel said:
Initially the expression A has 8 terms. So how is it reduced in the second line to 5 terms?
Could you show me, please?
Thank you.
\begin{align*}
A&=10^{28} -10^{22} +61\times10^{14}+12\times10^{21}-12\times10^{15}+3\times10^{9}-36\times10^{8}+9\times10^{2}\\
&=10^{28} +2\times10^{21}-59\times10^{14}-60\times10^{7}+9\times10^{2}
\end{align*}
Hi Sabeel, and welcome to MHB!

Here's a clue that might get you started. One of the terms in the first line is $-10^{22}$. You could write that as $-10\times 10^{21}$.
 
Opalg said:
Hi Sabeel, and welcome to MHB!

Here's a clue that might get you started. One of the terms in the first line is $-10^{22}$. You could write that as $-10\times 10^{21}$.

Thank you for welcoming me, and thank you for your answer.
Your hint is useful: $12^{21} - 10^{22} = 12^{21} -10\times 10^{21} =(12-10)10^{21}=2\times10^{21}$
I'll struggle with the others and report back.
 
$-12\times10^{15}+61\times10^{14}=-12\times10\times10^{14}=10^{14}(-120+61)=-59\times10^{14}$
$3\times10^{9}-36\times10^{8}=3\times10\times10^{8}-36\times10^{8}=10^8 (30-36)=-6\times10^{8}=-60\times10^{7}$

Your hint was more than useful. Thank you so much.
 
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