If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

Question

If  (\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}} , then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36

Bunuel · Accepted Answer

If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36

Step by step:

(\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}} ;

\frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2*2^{35}*5^{35}} ;

\frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2^{36}*5^{35}} ;

\frac{1}{5^m}= \frac{1}{5^{35}} ;

m=35 .

Answer: D.

Shortcut approach:

(\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*10^{35}} ;

\frac{1}{5^m}* (\frac{1}{4})^{18} = \frac{1}{2*2^{35}*5^{35}} .

Since there are only integers in the answer choices then we can concentrate only on the powers of 5: they should be equal on both sides:  m=35 .

Answer: D.

PareshGmat · Answer

\frac{1}{5^m} * \frac{1}{4^{18}} = \frac{1}{2*10^{35}}

Reciprocal the complete equation   ;    Get rid of the fraction

5^m * 2^{18*2} = 2 * 2^{35} * 5^{35}

5^m * 2^{36} = 2^{36} * 5^{35}

m = 35

Answer = D

domu904 · Answer

Thanks Bunnuel for the quick reply. So does that mean 1^m will always equal to 1? Because I was assuming m could be negative integer.

Bunuel · Answer

Yes, 1^m=1, for any m.

JeffTargetTestPrep · Answer

The negative exponent rule states: (1/a)^b can be re-expressed as a^(-b). Let’s flip all of the fractions using the negative exponent rule:

5^-m x 4^-18 = 2^-1 x 10^-35

5^-m x 2^-36 = 2^-1 x 2^-35 x 5^-35

5^-m x 2^-36 = 2^-36 x 5^-35

5^-m = 5^-35

m = 35

Answer: D

BrentGMATPrepNow · Answer

Exponent property #1: (\frac{a}{b})^k=\frac{a^k}{b^k} Exponent property #2: (b^x)^y = b^{xy} Exponent property #3: (ab)^x = a^xb^x ------------------------------------------------------ Given: (\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}} Applying exponent property#1, we get: Given: (\frac{1^m}{5^m})(\frac{1^{18}}{4^{18}}) = \frac{1}{2*(10)^{35}} Simplify to get: Given: (\frac{1}{5^m})(\frac{1}{4^{18}}) = \frac{1}{2*(10)^{35}} ASIDE: To determine the value of m, we must rewrite both sides of the equation with similar base. So, for the left side, we'll rewrite 4 as 2^2 For the right side, we'll rewrite 10 as 2 imes 5 We get: (\frac{1}{5^m})(\frac{1}{(2^2)^{18}}) = \frac{1}{2*(2 imes 5)^{35}} Applying exponent property#2, we get: (\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{2*(2 imes 5)^{35}} Applying exponent property#3, we get: (\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{2*(2^{35})(5^{35})} Since 2*(2^{35} = 2^{36} , we can write: (\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{(2^{36})(5^{35})} NOTE : Notice that I really didn't need to spend so much time working on the powers of 2, since the variable m was the exponent of 5. Had I focused solely on the powers of 5, I could have answered the question MUCH faster. That said, I wanted to show all of the exponent properties at work.

Cheers, Brent

Abhishek009 · Answer

5^{-m}*2^{-36} = 2^{-1}*2^{-35}*5^{-35}

5^{-m}*2^{-36} = 2^{-36}*5^{-35}

Or,  5^{-m} = 5^{-35}

Or,  m = 35 , Answer must be (D)

bumpbot · Answer

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If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

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If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

Prep Toolkit

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