Multiply or divide, as indicated. See Example 3. (15p³ / 9p²) ...

Question

Multiply or divide, as indicated. See Example 3. (15p³ / 9p²) • (12p / 10p³)

Accepted Answer

Hey, everyone here we are asked to perform the indicated operations and simplify for the following rational expression. 18 U cubed divided by 21 U squared multiplied by 42 U divided by three U cubed. Here we have four answer choice options, answer choice. A one divided by 12 U answer bu divided by 12, answer C 12 divided by U answer D 12 U. So before we begin multiplying both of our given fractions together, we want to start by reducing each fraction individually. So to reduce our fractions, we first want to recall the quotient rule for exponents which states that a raise to the power of M divided by a raise to the power of N is equivalent to a raise to the power of M minus N. So now utilizing this property, we can begin rewriting our fractions where our first term becomes 18, divided by 21 multiplied by U raised to the power of three minus two. And now with our second term, this first term is multiplied by 42 divided by three, multiplied by U raised to the power of one minus three. And now we can begin reducing both of the fractions along with the exponents of U. So first, we have 18 divided by 21 which reduces to six divided by seven. And this is multiplied by U raised to the power of one. And this term is multiplied by 42 divided by three, which reduces to 14, divided by one and multiplied by U raised to the power of negative two. So now that we have reduced both of our terms, we can begin multiplying them together. So for this, we now want to recall the product rule for exponents which states a raise to the power of M multiplied by a raise to the power of N is equivalent to a raise to the power of M plus N. So now utilizing this rule, we can start simplifying our two terms. So first multiplying the fractions, we again have six divided by seven multiplied by 14, divided by one. Well, here we see we have seven in the denominator and 14 in the numerator. So the 14 reduces and becomes two. So we now just have six multiplied by two. And then for our U terms, we have U raised to the power of one plus negative two. And so now we just want to continue simplifying our current expression. So six multiplied by two, gives us 12 multiplied by U raised to the power of negative one. And now our last step in simplifying is to recall that when we have a negative exponent, we can rewrite the term, the variable in the denominator to make it positive. So here we will have 12 divided by you with a positive exponent of one for you. And so now we have fully simplified our answer. And so we are left with answers, answer choice C where again, we have the expression 12 divided by you. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Multiply or divide, as indicated. See Example 3. (15p³ / 9p²) • (12p / 10p³)

Key Concepts

Multiplication and Division of Algebraic Fractions

Laws of Exponents

Simplification of Algebraic Expressions

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