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Problem 10 Easy Difficulty

For the following exercises, use like bases to solve the exponential equation.
$$
\left(\frac{1}{64}\right)^{3 n} \cdot 8=2^{6}
$$

Answer

$-\frac{1}{6}$

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Top Algebra Educators
Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

So here's a question. And first you need to recognize that, too, is our lowest common factor between 64 8 and two. So we're gonna cover everything to a base of two. So recognize here that also this is a fraction. So we're gonna raises to the negative power in order to bring the 64 to the numerator. And so 64 is two to the two to the six power. And since we need to branch, the new mayor is new to the negative six power or so to today, or six to the three end times, two to the third ukuleles to to the sixth. Okay, so when Ray's exponents to another power, we multiply them. So two to the negative 18 and times two to the third equals two to the sixth. When we multiply like bases, we can add their exponents. So negative 18 and plus three equals two to the sixth. Okay, so applying are the 1 to 1 property. Since to ensure the same base, we have negative 18 n plus three equals six tracked through from both sides E 18 and you close through to bye bye. Negative 18 and we get the answer. You could have won over six

Top Algebra Educators
Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor