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Which of the following is equal to 5^17 × 4^9?
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07 May 2022, 00:37
07 May 2022, 00:37
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Which of the following is equal to \(5^{17}× 4^{9}\)?
A. \(2 × 10^{13}\)
B. \(2 × 10^{17}\)
C. \(2 × 10^{20}\)
D. \(2 × 10^{26} \)
E. \(2 × 10^{36}\)
A. \(2 × 10^{13}\)
B. \(2 × 10^{17}\)
C. \(2 × 10^{20}\)
D. \(2 × 10^{26} \)
E. \(2 × 10^{36}\)
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Re: Which of the following is equal to 5^17 × 4^9?
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07 May 2022, 05:14
07 May 2022, 05:14
1
Carcass wrote:
Which of the following is equal to \(5^{17}× 4^{9}\)?
A. \(2 × 10^{13}\)
B. \(2 × 10^{17}\)
C. \(2 × 10^{20}\)
D. \(2 × 10^{26} \)
E. \(2 × 10^{36}\)
A. \(2 × 10^{13}\)
B. \(2 × 10^{17}\)
C. \(2 × 10^{20}\)
D. \(2 × 10^{26} \)
E. \(2 × 10^{36}\)
Key property: \((x^n)(y^n) = (xy)^n\)
Example: \((3^7)(10^7) = 30^7\)
Strategy: When I check the answer choices, I see that they're all in the same form. Since I know that 2 x 5 = 10, I'm going to apply the above property after I rewrite \(4\) as \(2^2\)
Given: \(5^{17}× 4^{9}\)
Rewrite \(4\) as follows: \(5^{17}× (2^2)^{9}\)
Simplify by applying the power of a power law: \(5^{17}× 2^{18}\)
Strategy: In order to apply the how about property, we need the same exponent for bases 5 and 2. We can do this by rewriting \(2^{18}\) as \(2^{17} × 2^1\)
Rewrite \(2^{18}\) as follows: \(5^{17}× 2^{17} × 2^1\)
Apply the above property to get: \(10^{17} × 2^1\)
Answer: B
gmatclubot
Re: Which of the following is equal to 5^17 × 4^9? [#permalink]
07 May 2022, 05:14
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