QuestionSimplify $2\left(a^{2} b^{-1}\right)$ and express with positive exponents.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(a^{} b^{-1}\right)$ . We need to simplify the expression using the properties of exponents3. In the final answer, only positive exponents should be included

STEP 2

First, we distribute the2 across the terms inside the parentheses.
$2\left(a^{2} b^{-1}\right) =2a^{2} \cdot2b^{-1}$

STEP 3

Next, we simplify the expression by multiplying the coefficients.
$2a^{2} \cdot2b^{-1} =a^{2}b^{-1}$

STEP 4

Now, we need to convert the negative exponent to a positive exponent. We can do this by taking the reciprocal of the base.
$4a^{2}b^{-1} =4a^{2} \cdot \frac{1}{b^{1}}$

STEP 5

Finally, we rewrite the expression to only include positive exponents.
$4a^{2} \cdot \frac{1}{b^{1}} = \frac{4a^{2}}{b}$ So, the simplified expression is $\frac{4a^{2}}{b}$ .

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QuestionSimplify $2\left(a^{2} b^{-1}\right)$ and express with positive exponents.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(a^{} b^{-1}\right)$ . We need to simplify the expression using the properties of exponents3. In the final answer, only positive exponents should be included

STEP 2

First, we distribute the2 across the terms inside the parentheses.
$2\left(a^{2} b^{-1}\right) =2a^{2} \cdot2b^{-1}$

STEP 3

Next, we simplify the expression by multiplying the coefficients.
$2a^{2} \cdot2b^{-1} =a^{2}b^{-1}$

STEP 4

Now, we need to convert the negative exponent to a positive exponent. We can do this by taking the reciprocal of the base.
$4a^{2}b^{-1} =4a^{2} \cdot \frac{1}{b^{1}}$

STEP 5

Finally, we rewrite the expression to only include positive exponents.
$4a^{2} \cdot \frac{1}{b^{1}} = \frac{4a^{2}}{b}$ So, the simplified expression is $\frac{4a^{2}}{b}$ .

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QuestionSimplify 2(a2b−1)2\left(a^{2} b^{-1}\right)2(a2b−1) and express with positive exponents.

Studdy Solution

STEP 1

Assumptions1. We are given the expression (ab−1)\left(a^{} b^{-1}\right)(ab−1). We need to simplify the expression using the properties of exponents3. In the final answer, only positive exponents should be included

STEP 2

First, we distribute the2 across the terms inside the parentheses.2(a2b−1)=2a2⋅2b−12\left(a^{2} b^{-1}\right) =2a^{2} \cdot2b^{-1}2(a2b−1)=2a2⋅2b−1

STEP 3

Next, we simplify the expression by multiplying the coefficients.2a2⋅2b−1=a2b−12a^{2} \cdot2b^{-1} =a^{2}b^{-1}2a2⋅2b−1=a2b−1

STEP 4

Now, we need to convert the negative exponent to a positive exponent. We can do this by taking the reciprocal of the base.4a2b−1=4a2⋅1b14a^{2}b^{-1} =4a^{2} \cdot \frac{1}{b^{1}}4a2b−1=4a2⋅b11​

STEP 5

Finally, we rewrite the expression to only include positive exponents.4a2⋅1b1=4a2b4a^{2} \cdot \frac{1}{b^{1}} = \frac{4a^{2}}{b}4a2⋅b11​=b4a2​So, the simplified expression is 4a2b\frac{4a^{2}}{b}b4a2​.

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QuestionSimplify $2\left(a^{2} b^{-1}\right)$ and express with positive exponents.

Assumptions1. We are given the expression $\left(a^{} b^{-1}\right)$ . We need to simplify the expression using the properties of exponents3. In the final answer, only positive exponents should be included

First, we distribute the2 across the terms inside the parentheses.
$2\left(a^{2} b^{-1}\right) =2a^{2} \cdot2b^{-1}$

Next, we simplify the expression by multiplying the coefficients.
$2a^{2} \cdot2b^{-1} =a^{2}b^{-1}$

Now, we need to convert the negative exponent to a positive exponent. We can do this by taking the reciprocal of the base.
$4a^{2}b^{-1} =4a^{2} \cdot \frac{1}{b^{1}}$

Finally, we rewrite the expression to only include positive exponents.
$4a^{2} \cdot \frac{1}{b^{1}} = \frac{4a^{2}}{b}$ So, the simplified expression is $\frac{4a^{2}}{b}$ .