Question Simplify $y^{\frac{7}{4}} / y^{\frac{11}{4}}$ assuming positive variables. Express answer as $A$ or $A/B$ with positive exponents.

Studdy Solution

STEP 1

Assumptions
1. All variables are positive.
2. We are simplifying the expression $\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}}$ .
3. We will use the laws of exponents to simplify the expression.

STEP 2

To simplify the expression, we use the law of exponents that states when dividing like bases, we subtract the exponents.
$\frac{y^a}{y^b} = y^{a-b}$

STEP 3

Apply the law of exponents to the given expression.
$\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = y^{\frac{7}{4} - \frac{11}{4}}$

STEP 4

Subtract the exponents.
$y^{\frac{7}{4} - \frac{11}{4}} = y^{-1}$

STEP 5

Since we want all exponents to be positive, we use the law of exponents that states $y^{-a} = \frac{1}{y^a}$ .
$y^{-1} = \frac{1}{y}$

STEP 6

Write the final simplified expression with a positive exponent.
$\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = \frac{1}{y}$
The simplified expression is $\frac{1}{y}$ .

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Question Simplify $y^{\frac{7}{4}} / y^{\frac{11}{4}}$ assuming positive variables. Express answer as $A$ or $A/B$ with positive exponents.

Studdy Solution

STEP 1

Assumptions
1. All variables are positive.
2. We are simplifying the expression $\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}}$ .
3. We will use the laws of exponents to simplify the expression.

STEP 2

To simplify the expression, we use the law of exponents that states when dividing like bases, we subtract the exponents.
$\frac{y^a}{y^b} = y^{a-b}$

STEP 3

Apply the law of exponents to the given expression.
$\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = y^{\frac{7}{4} - \frac{11}{4}}$

STEP 4

Subtract the exponents.
$y^{\frac{7}{4} - \frac{11}{4}} = y^{-1}$

STEP 5

Since we want all exponents to be positive, we use the law of exponents that states $y^{-a} = \frac{1}{y^a}$ .
$y^{-1} = \frac{1}{y}$

STEP 6

Write the final simplified expression with a positive exponent.
$\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = \frac{1}{y}$
The simplified expression is $\frac{1}{y}$ .

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Question Simplify y74/y114y^{\frac{7}{4}} / y^{\frac{11}{4}}y47​/y411​ assuming positive variables. Express answer as AAA or A/BA/BA/B with positive exponents.

Studdy Solution

STEP 1

Assumptions1. All variables are positive.2. We are simplifying the expression y74y114\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}}y411​y47​​.3. We will use the laws of exponents to simplify the expression.

STEP 2

To simplify the expression, we use the law of exponents that states when dividing like bases, we subtract the exponents.yayb=ya−b\frac{y^a}{y^b} = y^{a-b}ybya​=ya−b

STEP 3

Apply the law of exponents to the given expression.y74y114=y74−114\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = y^{\frac{7}{4} - \frac{11}{4}}y411​y47​​=y47​−411​

STEP 4

Subtract the exponents.y74−114=y−1y^{\frac{7}{4} - \frac{11}{4}} = y^{-1}y47​−411​=y−1

STEP 5

Since we want all exponents to be positive, we use the law of exponents that states y−a=1yay^{-a} = \frac{1}{y^a}y−a=ya1​.y−1=1yy^{-1} = \frac{1}{y}y−1=y1​

STEP 6

Write the final simplified expression with a positive exponent.y74y114=1y\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = \frac{1}{y}y411​y47​​=y1​The simplified expression is 1y\frac{1}{y}y1​.

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Question Simplify $y^{\frac{7}{4}} / y^{\frac{11}{4}}$ assuming positive variables. Express answer as $A$ or $A/B$ with positive exponents.

Assumptions
1. All variables are positive.
2. We are simplifying the expression $\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}}$ .
3. We will use the laws of exponents to simplify the expression.

To simplify the expression, we use the law of exponents that states when dividing like bases, we subtract the exponents.
$\frac{y^a}{y^b} = y^{a-b}$

Apply the law of exponents to the given expression.
$\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = y^{\frac{7}{4} - \frac{11}{4}}$

Subtract the exponents.
$y^{\frac{7}{4} - \frac{11}{4}} = y^{-1}$

Since we want all exponents to be positive, we use the law of exponents that states $y^{-a} = \frac{1}{y^a}$ .
$y^{-1} = \frac{1}{y}$

Write the final simplified expression with a positive exponent.
$\frac{y^{\frac{7}{4}}}{y^{\frac{11}{4}}} = \frac{1}{y}$
The simplified expression is $\frac{1}{y}$ .