QuestionSimplify $\frac{y^{9} \cdot y^{8}}{y^{4}}$ . What is the result? a. $\frac{1}{y^{13}}$ b. $y^{5}$ c. $\frac{1}{y^{5}}$ d. $y^{13}$

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{y^{9} \cdot y^{8}}{y^{4}}$ . We need to simplify this expression and select the correct option from the given choices

STEP 2

First, we need to simplify the numerator of the expression. We can do this by adding the exponents of $y$ in the numerator, as per the rule of exponents which states that $a^{m} \cdot a^{n} = a^{m+n}$ .
$y^{9} \cdot y^{8} = y^{9+8}$

STEP 3

Now, plug in the given values for the exponents to calculate the new exponent.
$y^{9} \cdot y^{8} = y^{9+8} = y^{17}$

STEP 4

Now, we have the simplified numerator. The expression becomes $\frac{y^{17}}{y^{4}}$ .

STEP 5

Next, we need to simplify the entire expression. We can do this by subtracting the exponent of $y$ in the denominator from the exponent of $y$ in the numerator, as per the rule of exponents which states that $\frac{a^{m}}{a^{n}} = a^{m-n}$ .
$\frac{y^{17}}{y^{4}} = y^{17-4}$

STEP 6

Now, plug in the given values for the exponents to calculate the new exponent.
$\frac{y^{17}}{y^{4}} = y^{17-4} = y^{13}$ The simplified expression is $y^{13}$ , which matches option d.
So, the correct answer is option d. $y^{13}$ .

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QuestionSimplify $\frac{y^{9} \cdot y^{8}}{y^{4}}$ . What is the result? a. $\frac{1}{y^{13}}$ b. $y^{5}$ c. $\frac{1}{y^{5}}$ d. $y^{13}$

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{y^{9} \cdot y^{8}}{y^{4}}$ . We need to simplify this expression and select the correct option from the given choices

STEP 2

First, we need to simplify the numerator of the expression. We can do this by adding the exponents of $y$ in the numerator, as per the rule of exponents which states that $a^{m} \cdot a^{n} = a^{m+n}$ .
$y^{9} \cdot y^{8} = y^{9+8}$

STEP 3

Now, plug in the given values for the exponents to calculate the new exponent.
$y^{9} \cdot y^{8} = y^{9+8} = y^{17}$

STEP 4

Now, we have the simplified numerator. The expression becomes $\frac{y^{17}}{y^{4}}$ .

STEP 5

Next, we need to simplify the entire expression. We can do this by subtracting the exponent of $y$ in the denominator from the exponent of $y$ in the numerator, as per the rule of exponents which states that $\frac{a^{m}}{a^{n}} = a^{m-n}$ .
$\frac{y^{17}}{y^{4}} = y^{17-4}$

STEP 6

Now, plug in the given values for the exponents to calculate the new exponent.
$\frac{y^{17}}{y^{4}} = y^{17-4} = y^{13}$ The simplified expression is $y^{13}$ , which matches option d.
So, the correct answer is option d. $y^{13}$ .

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QuestionSimplify y9⋅y8y4\frac{y^{9} \cdot y^{8}}{y^{4}}y4y9⋅y8​. What is the result? a. 1y13\frac{1}{y^{13}}y131​ b. y5y^{5}y5 c. 1y5\frac{1}{y^{5}}y51​ d. y13y^{13}y13

Studdy Solution

STEP 1

Assumptions1. We are given the expression y9⋅y8y4\frac{y^{9} \cdot y^{8}}{y^{4}}y4y9⋅y8​ . We need to simplify this expression and select the correct option from the given choices

STEP 2

First, we need to simplify the numerator of the expression. We can do this by adding the exponents of yyy in the numerator, as per the rule of exponents which states that am⋅an=am+na^{m} \cdot a^{n} = a^{m+n}am⋅an=am+n.y9⋅y8=y9+8y^{9} \cdot y^{8} = y^{9+8}y9⋅y8=y9+8

STEP 3

Now, plug in the given values for the exponents to calculate the new exponent.y9⋅y8=y9+8=y17y^{9} \cdot y^{8} = y^{9+8} = y^{17}y9⋅y8=y9+8=y17

STEP 4

Now, we have the simplified numerator. The expression becomes y17y4\frac{y^{17}}{y^{4}}y4y17​.

STEP 5

STEP 6

Now, plug in the given values for the exponents to calculate the new exponent.y17y4=y17−4=y13\frac{y^{17}}{y^{4}} = y^{17-4} = y^{13}y4y17​=y17−4=y13The simplified expression is y13y^{13}y13, which matches option d.So, the correct answer is option d. y13y^{13}y13.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSimplify $\frac{y^{9} \cdot y^{8}}{y^{4}}$ . What is the result? a. $\frac{1}{y^{13}}$ b. $y^{5}$ c. $\frac{1}{y^{5}}$ d. $y^{13}$

Assumptions1. We are given the expression $\frac{y^{9} \cdot y^{8}}{y^{4}}$ . We need to simplify this expression and select the correct option from the given choices

First, we need to simplify the numerator of the expression. We can do this by adding the exponents of $y$ in the numerator, as per the rule of exponents which states that $a^{m} \cdot a^{n} = a^{m+n}$ .
$y^{9} \cdot y^{8} = y^{9+8}$

Now, plug in the given values for the exponents to calculate the new exponent.
$y^{9} \cdot y^{8} = y^{9+8} = y^{17}$

Now, we have the simplified numerator. The expression becomes $\frac{y^{17}}{y^{4}}$ .

Now, plug in the given values for the exponents to calculate the new exponent.
$\frac{y^{17}}{y^{4}} = y^{17-4} = y^{13}$ The simplified expression is $y^{13}$ , which matches option d.
So, the correct answer is option d. $y^{13}$ .