Math solving exponential equations

Test Preparation SAT Preparation
1

<p>If n>0 and (8^(4/n))^(-3) = (2^(-n))^(3/4) , then n equals</p>

<p>(A) 12√3
(B) 8
(C) 4√3
(D) 4
(E) 2√3</p>

<p>Plugging in the answers is too tedious for this one. How do you solve it algebraically?</p>

2

<p>Raising an exponent to an exponent requires that you multiply the powers. 8 = 2^3.</p>

3

<p>OMG ty 4 ur help =) <3333 xoxoxo</p>

4

<p>If n>0 and (8^(4/n))^(-3) = (2^(-n))^(3/4) , then n equals</p>

<p>(A) 12√3
(B) 8
(C) 4√3
(D) 4
(E) 2√3</p>

<p>(8^(4/n))^(-3) = 8^(-12/n) = 2^(3)^(-12/n) = 2^(-36/n)</p>

<p>2^-n^(3/4) = 2^(-3n/4)</p>

<p>2^(-36/n) = 2^(-3n/4)</p>

<p>(36/n) = (3n/4)</p>

<p>n = SQRT(48)</p>

<p>n = 4SQRT(3)</p>

<p>The answer is (C)</p>