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Which of the following is closest to the value of (2^23)(5^26)?

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Which of the following is closest to the value of (2^23)(5^26)?  [#permalink]

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New post 24 Nov 2016, 03:03
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A
B
C
D
E

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Re: Which of the following is closest to the value of (2^23)(5^26)?  [#permalink]

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New post 24 Nov 2016, 03:21
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Bunuel wrote:
Which of the following is closest to the value of (2^23)(5^26)?

A. 10^23
B. 10^24
C. 10^25
D. 10^26
E. 10^27


\(2^{23} \times 5^{26}=2^{23} \times 5^{23} \times 5^3=10^{23} \times 125 \approx 10^{23} \times 100 = 10^{25}\)

The answer is C.
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Re: Which of the following is closest to the value of (2^23)(5^26)?  [#permalink]

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New post 13 Aug 2018, 02:33
Hi guys,

Just wanted to check the rule here with you.
"When two numbers have the same exponent, I can multiply the numbers together and keep the exponent as it was for the two numbers." Is this correct?
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Which of the following is closest to the value of (2^23)(5^26)?  [#permalink]

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New post 13 Aug 2018, 02:40
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loneo3006 wrote:
Hi guys,

Just wanted to check the rule here with you.
"When two numbers have the same exponent, I can multiply the numbers together and keep the exponent as it was for the two numbers." Is this correct?


EXPONENTS

Exponents are a "shortcut" method of showing a number that was multiplied by itself several times. For instance, number \(a\) multiplied \(n\) times can be written as \(a^n\), where \(a\) represents the base, the number that is multiplied by itself \(n\) times and \(n\) represents the exponent. The exponent indicates how many times to multiple the base, \(a\), by itself.

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 \((a^m)^n\) (if exponentiation is indicated by stacked symbols, the rule is to work from the top down)

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:
\(a^{\frac{1}{n}}=\sqrt[n]{a}\)

\(a^{\frac{m}{n}}=\sqrt[n]{a^m}\)


ROOTS

Roots (or radicals) are the "opposite" operation of applying exponents. For instance x^2=16 and square root of 16=4.

General rules:
• \(\sqrt{x}\sqrt{y}=\sqrt{xy}\) and \(\frac{\sqrt{x}}{\sqrt{y}}=\sqrt{\frac{x}{y}}\).

• \((\sqrt{x})^n=\sqrt{x^n}\)

• \(x^{\frac{1}{n}}=\sqrt[n]{x}\)

• \(x^{\frac{n}{m}}=\sqrt[m]{x^n}\)

• \({\sqrt{a}}+{\sqrt{b}}\neq{\sqrt{a+b}}\)

• \(\sqrt{x^2}=|x|\), when \(x\leq{0}\), then \(\sqrt{x^2}=-x\) and when \(x\geq{0}\), then \(\sqrt{x^2}=x\)

• When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

• Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

8. Exponents and Roots of Numbers



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Which of the following is closest to the value of (2^23)(5^26)?  [#permalink]

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New post 13 Aug 2018, 02:46
Thanks,

this was the one I was looking for :

Operations involving the same exponents:
Keep the exponent, multiply or divide the bases
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Re: Which of the following is closest to the value of (2^23)(5^26)?  [#permalink]

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New post 18 Aug 2018, 19:33
Bunuel wrote:
Which of the following is closest to the value of (2^23)(5^26)?

A. 10^23
B. 10^24
C. 10^25
D. 10^26
E. 10^27


Simplifying, we have:

2^23 x 5^23 x 5^3

10^23 x 5^3, which is about 10^23 x 10^2 = 10^25.

Answer: C
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Re: Which of the following is closest to the value of (2^23)(5^26)?   [#permalink] 18 Aug 2018, 19:33
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