Math / Algebra

QuestionUse the quotient rule to simplify. $\frac{x^{4} y^{7}}{x^{2} y^{7}}$

Studdy Solution

STEP 1

1. We are simplifying a rational expression using the quotient rule.
2. The quotient rule for exponents states that $\frac{a^m}{a^n} = a^{m-n}$ when $a \neq 0$ .
3. The expression involves variables $x$ and $y$ with exponents.

STEP 2

1. Apply the quotient rule to the variable $x$ .
2. Apply the quotient rule to the variable $y$ .
3. Simplify the expression.

STEP 3

Apply the quotient rule to the variable $x$ :
$\frac{x^4}{x^2} = x^{4-2} = x^2$

STEP 4

Apply the quotient rule to the variable $y$ :
$\frac{y^7}{y^7} = y^{7-7} = y^0$ Since $y^0 = 1$ , this simplifies to 1.

STEP 5

Combine the simplified results from the previous steps:
$\frac{x^4 y^7}{x^2 y^7} = x^2 \cdot 1 = x^2$
The simplified expression is:
$\boxed{x^2}$

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QuestionUse the quotient rule to simplify. $\frac{x^{4} y^{7}}{x^{2} y^{7}}$

Studdy Solution

STEP 1

1. We are simplifying a rational expression using the quotient rule.
2. The quotient rule for exponents states that $\frac{a^m}{a^n} = a^{m-n}$ when $a \neq 0$ .
3. The expression involves variables $x$ and $y$ with exponents.

STEP 2

1. Apply the quotient rule to the variable $x$ .
2. Apply the quotient rule to the variable $y$ .
3. Simplify the expression.

STEP 3

Apply the quotient rule to the variable $x$ :
$\frac{x^4}{x^2} = x^{4-2} = x^2$

STEP 4

Apply the quotient rule to the variable $y$ :
$\frac{y^7}{y^7} = y^{7-7} = y^0$ Since $y^0 = 1$ , this simplifies to 1.

STEP 5

Combine the simplified results from the previous steps:
$\frac{x^4 y^7}{x^2 y^7} = x^2 \cdot 1 = x^2$
The simplified expression is:
$\boxed{x^2}$

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QuestionUse the quotient rule to simplify. x4y7x2y7\frac{x^{4} y^{7}}{x^{2} y^{7}}x2y7x4y7​

Studdy Solution

STEP 1

1. We are simplifying a rational expression using the quotient rule.2. The quotient rule for exponents states that aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n when a≠0a \neq 0a=0.3. The expression involves variables xxx and yyy with exponents.

STEP 2

1. Apply the quotient rule to the variable xxx.2. Apply the quotient rule to the variable yyy.3. Simplify the expression.

STEP 3

Apply the quotient rule to the variable xxx:x4x2=x4−2=x2\frac{x^4}{x^2} = x^{4-2} = x^2x2x4​=x4−2=x2

STEP 4

Apply the quotient rule to the variable yyy:y7y7=y7−7=y0\frac{y^7}{y^7} = y^{7-7} = y^0y7y7​=y7−7=y0 Since y0=1y^0 = 1y0=1, this simplifies to 1.

STEP 5

Combine the simplified results from the previous steps:x4y7x2y7=x2⋅1=x2\frac{x^4 y^7}{x^2 y^7} = x^2 \cdot 1 = x^2x2y7x4y7​=x2⋅1=x2The simplified expression is:x2\boxed{x^2}x2​

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QuestionUse the quotient rule to simplify. $\frac{x^{4} y^{7}}{x^{2} y^{7}}$

1. We are simplifying a rational expression using the quotient rule.
2. The quotient rule for exponents states that $\frac{a^m}{a^n} = a^{m-n}$ when $a \neq 0$ .
3. The expression involves variables $x$ and $y$ with exponents.

1. Apply the quotient rule to the variable $x$ .
2. Apply the quotient rule to the variable $y$ .
3. Simplify the expression.

Apply the quotient rule to the variable $x$ :
$\frac{x^4}{x^2} = x^{4-2} = x^2$

Apply the quotient rule to the variable $y$ :
$\frac{y^7}{y^7} = y^{7-7} = y^0$ Since $y^0 = 1$ , this simplifies to 1.

Combine the simplified results from the previous steps:
$\frac{x^4 y^7}{x^2 y^7} = x^2 \cdot 1 = x^2$
The simplified expression is:
$\boxed{x^2}$