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28 Sep 2010, 07:41
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Can some one fill the blanks for these queries
0 ^ 0 =
0 ^ 1 =
0 ^ n where n > 1 =
2 ^ root(2) =
root (3) ^ root(3) =
Most likely we wont encounter them but in DS it might come up i am not sure
0 ^ 0 =
0 ^ 1 =
0 ^ n where n > 1 =
2 ^ root(2) =
root (3) ^ root(3) =
Most likely we wont encounter them but in DS it might come up i am not sure
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28 Sep 2010, 08:00
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rxs0005
Exponents one and zero:
\(a^0=1\) Any nonzero number to the power of 0 is 1.
For example: \(5^0=1\) and \((-3)^0=1\)
• Note: the case of 0^0 is not tested on the GMAT.
\(a^1=a\) Any number to the power 1 is itself.
Powers of zero:
If the exponent is positive, the power of zero is zero: \(0^n = 0\), where \(n > 0\).
If the exponent is negative, the power of zero (\(0^n\), where \(n < 0\)) is undefined, because division by zero is implied.
Powers of one:
\(1^n=1\) The integer powers of one are one.
Negative powers:
\(a^{-n}=\frac{1}{a^n}\)
Powers of minus one:
If n is an even integer, then \((-1)^n=1\).
If n is an odd integer, then \((-1)^n =-1\).
Operations involving the same exponents:
Keep the exponent, multiply or divide the bases
\(a^n*b^n=(ab)^n\)
\(\frac{a^n}{b^n}=(\frac{a}{b})^n\)
\((a^m)^n=a^{mn}\)
\(a^m^n=a^{(m^n)}\) and not \((a^m)^n\)
Operations involving the same bases:
Keep the base, add or subtract the exponent (add for multiplication, subtract for division)
\(a^n*a^m=a^{n+m}\)
\(\frac{a^n}{a^m}=a^{n-m}\)
Fraction as power:
\(a^{\frac{1}{n}}=\sqrt[n]{a}\)
\(a^{\frac{m}{n}}=\sqrt[n]{a^m}\)
For more on Number properties check: math-number-theory-88376.html
Hope it helps.
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
