Multiply or divide, as indicated. (y^3 + y^2)/7 * 49/(y^4 + y^3)

Question

Accepted Answer

Hey everyone here we are asked to multiply and simplify the given expression. Where we have the quantity of G to the fifth power plus G to the sixth power divided by 11 times 121 divided by the quantity of G to the sixth power plus G to the seventh power. Now our first step here in simplifying this expression is to just group together our variables in group together our numbers. So doing this, our first fraction now becomes the quantity of G. To the fifth power plus G. To the sixth power divided by the quantity of G. Two. The six power plus G to the seventh power. In our second fraction where we now group Together the numbers we have 121 divided by 11. So now we just want to begin simplifying and we can do this with our first fraction by first factoring out the highest power of G possible. So beginning in our numerator we have the highest power of G. That we can factor out is just five. So we can fact out G. To the fifth power. Which leaves us with G. To the fifth power times the quantity of one plus G. And now we repeat this in our denominator. But in the denominator the highest power of which we can factor out is six. So we have G to the six power times the quantity of one plus G. And now for our second fraction where we had divided by 11. Well dividing the numerator by the denominator just simplifies to 11. So now we can further simplify our first fraction by performing some cancelations. So we can see that in the numerator we have one plus G. Which also appears in the denominator. So both of these terms cancel out. And so now we are left with G. To the with power divided by G. To the six power then times 11. And so now that we are dividing two exponents of the same base. We need to recall the quotient rule for exponents which tells us that A. To the power of N divided by A. To the power of M. Is equal to A. To the power of N minus M. So now we can rewrite our expression using this exponent rule. So we have G to the power of five minus six and then times 11. And so now we just need to simplify our exponent here. So we are left with G. To the power of negative one then times 11. But now we need to finish simplifying by recalling the exponents rule for a negative exponents which tells us that A. To the power of negative N. is equivalent to one divided by a. To the power of positive n. So here we see that our negative exponents is this negative one for G. So we can rewrite our expression using this exponent rule. So we are left with 11 divided by G. And with this we have found our fully simplified form of our original expression and we are left with answer choice. A thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Multiply or divide, as indicated. (y^3 + y^2)/7 * 49/(y^4 + y^3)

Key Concepts

Polynomial Expressions

Factoring

Rational Expressions

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