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Use rules for exponents to simplify each expression.$$\frac{(-3 a)^{12}}{(-3 a)^{10}}$$
$9 a^{2}$
Algebra
Chapter 5
Exponents and Polynomials
Section 1
Rules for Exponents
Polynomials
Oregon State University
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
Lectures
01:32
In mathematics, the absolu…
01:11
00:39
Use the rules of exponents…
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00:46
Use the power rule for exp…
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01:00
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02:04
Use rules for exponents to…
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Use the properties of expo…
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In the following exercises…
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We need to simplify the given expression using the rule for exponents. The given expression is minus 3, a the whole power 12 divided by minus 38, the whole power 10 point. We know that the question rule for exponents states that a power by a power can be written as a power m minus m. So let us apply the quotient rule to simplify keeping the base. Let us subtract the exponents. It is 12 minus 10 point, so on simplifying this we get minus 3 a the whole square. We know that the power of a product- true for exponents states that if a product x y is raised to power, it can be written as x, power into y power, so using the power of product rule raise each factor of the product to power 2. So we get minus 3 raised to power 2 into a raised to power 2, so the value of minus 3 square is 9 and this is a square. Hence the solution is 9, a square.
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