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anonymous
 one year ago
What is the missing value?
3^6/3^?=3^4
A.
−10
B.
−2
C.
2
D.
10
anonymous
 one year ago
What is the missing value? 3^6/3^?=3^4 A. −10 B. −2 C. 2 D. 10

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whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{3^{6}}{3^?} = 3^4\] Remember that \[\frac{a^m}{a^n} = a^{mn}\]

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0So that means \[\frac{3^{6}}{3^?} = 3^{6?} = 3^4\]or \[6?=4\]Can you solve for ?

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0The exponent needs to be a number such that 6 <some number> = 4. Maybe you're confused because I didn't use a typical variable name, like \(x\). \[6x = 4\] Can you solve that for \(x\)? \(x\) is the exponent for the number in the denominator in the problem.

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.0Or, you could solve it a different way: \[\frac{3^{6}}{3^x} = 3^4\]Let's multiply both sides by \(3^x\): \[3^x*\frac{3^{6}}{3^x} = 3^4*3^x\]\[\cancel{3^x*}\frac{3^{6}}{\cancel{3^x}} = 3^4*3^x\]\[3^{6} = 3^4*3^x\] Now when we multiply exponentials with the same base, as we have here (everything is 3 to some power, 3 is the base), we keep the base and ADD the exponents. \[3^2*3^3 = 3^{2+3} = 3^5\]just like if we did it the long way:\[3^2*3^3=(3*3)*(3*3*3) = 3*3*3*3*3=3^5\] so \[3^{6}=3^4*3^x \]\[3^{6} = 3^{4+x}\]and the only way that can be true is if \[6 = 4+x\] Solve for \(x\) and you have your answer.
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