QuestionSimplify: $x^{3} y^{3} / x^{3} y^{2}$ . Choose the correct answer: a. $x y$ , b. $x$ , c. $y$ , d. $x y / x$ .

Studdy Solution

STEP 1

Assumptions1. The expression is $x^{3} y^{3} / x^{3} y^{}$ . We are asked to simplify the expression3. The rules of exponents apply, specifically the rule that states $a^{m} / a^{n} = a^{m-n}$

STEP 2

We can simplify the expression by applying the rule of exponents separately to the $x$ terms and the $y$ terms.
$x^{} y^{} / x^{} y^{2} = x^{-} y^{-2}$

STEP 3

Subtract the exponents to simplify the expression.
$x^{3-3} y^{3-2} = x^{0} y^{1}$

STEP 4

Any number (except zero) raised to the power of zero is1. Therefore, $x^{0} =1$ . Substitute this into the expression.
$x^{0} y^{1} =1 \cdot y^{1}$

STEP 5

implify the expression.
$1 \cdot y^{1} = y$ So, the simplified form of $x^{3} y^{3} / x^{3} y^{2}$ is $y$ .

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QuestionSimplify: $x^{3} y^{3} / x^{3} y^{2}$ . Choose the correct answer: a. $x y$ , b. $x$ , c. $y$ , d. $x y / x$ .

Studdy Solution

STEP 1

Assumptions1. The expression is $x^{3} y^{3} / x^{3} y^{}$ . We are asked to simplify the expression3. The rules of exponents apply, specifically the rule that states $a^{m} / a^{n} = a^{m-n}$

STEP 2

We can simplify the expression by applying the rule of exponents separately to the $x$ terms and the $y$ terms.
$x^{} y^{} / x^{} y^{2} = x^{-} y^{-2}$

STEP 3

Subtract the exponents to simplify the expression.
$x^{3-3} y^{3-2} = x^{0} y^{1}$

STEP 4

Any number (except zero) raised to the power of zero is1. Therefore, $x^{0} =1$ . Substitute this into the expression.
$x^{0} y^{1} =1 \cdot y^{1}$

STEP 5

implify the expression.
$1 \cdot y^{1} = y$ So, the simplified form of $x^{3} y^{3} / x^{3} y^{2}$ is $y$ .

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QuestionSimplify: x3y3/x3y2x^{3} y^{3} / x^{3} y^{2}x3y3/x3y2. Choose the correct answer: a. xyx yxy, b. xxx, c. yyy, d. xy/xx y / xxy/x.

Studdy Solution

STEP 1

Assumptions1. The expression is x3y3/x3yx^{3} y^{3} / x^{3} y^{}x3y3/x3y . We are asked to simplify the expression3. The rules of exponents apply, specifically the rule that states am/an=am−na^{m} / a^{n} = a^{m-n}am/an=am−n

STEP 2

We can simplify the expression by applying the rule of exponents separately to the xxx terms and the yyy terms.xy/xy2=x−y−2x^{} y^{} / x^{} y^{2} = x^{-} y^{-2}xy/xy2=x−y−2

STEP 3

Subtract the exponents to simplify the expression.x3−3y3−2=x0y1x^{3-3} y^{3-2} = x^{0} y^{1}x3−3y3−2=x0y1

STEP 4

Any number (except zero) raised to the power of zero is1. Therefore, x0=1x^{0} =1x0=1. Substitute this into the expression.x0y1=1⋅y1x^{0} y^{1} =1 \cdot y^{1}x0y1=1⋅y1

STEP 5

implify the expression.1⋅y1=y1 \cdot y^{1} = y1⋅y1=ySo, the simplified form of x3y3/x3y2x^{3} y^{3} / x^{3} y^{2}x3y3/x3y2 is yyy.

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QuestionSimplify: $x^{3} y^{3} / x^{3} y^{2}$ . Choose the correct answer: a. $x y$ , b. $x$ , c. $y$ , d. $x y / x$ .

Assumptions1. The expression is $x^{3} y^{3} / x^{3} y^{}$ . We are asked to simplify the expression3. The rules of exponents apply, specifically the rule that states $a^{m} / a^{n} = a^{m-n}$

We can simplify the expression by applying the rule of exponents separately to the $x$ terms and the $y$ terms.
$x^{} y^{} / x^{} y^{2} = x^{-} y^{-2}$

Subtract the exponents to simplify the expression.
$x^{3-3} y^{3-2} = x^{0} y^{1}$

Any number (except zero) raised to the power of zero is1. Therefore, $x^{0} =1$ . Substitute this into the expression.
$x^{0} y^{1} =1 \cdot y^{1}$

implify the expression.
$1 \cdot y^{1} = y$ So, the simplified form of $x^{3} y^{3} / x^{3} y^{2}$ is $y$ .