Math / Algebra

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Fractions / Fractions
Fractional
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If the expression $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ is written in the form $a x^{b} y^{c}$ , then what is the product of $a, b$ and $c$ ?
Answer Attempt 1 out of 2 $\square$ Submit Answer

Studdy Solution

STEP 1

1. The given expression is $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ .
2. We need to express this in the form $a x^{b} y^{c}$ .
3. We will then find the product of $a$ , $b$ , and $c$ .

STEP 2

1. Simplify the expression under the square root.
2. Simplify the entire expression $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ .
3. Identify the values of $a$ , $b$ , and $c$ .
4. Calculate the product of $a$ , $b$ , and $c$ .

STEP 3

Simplify the expression under the square root:
$\sqrt{x y^{5}} = (x y^{5})^{1/2} = x^{1/2} y^{5/2}$

STEP 4

Substitute the simplified square root expression back into the original expression:
$4 x^{-3} y^{-1} \cdot x^{1/2} y^{5/2}$

STEP 5

Combine the powers of $x$ and $y$ :
$4 \cdot x^{-3 + 1/2} \cdot y^{-1 + 5/2}$
$= 4 \cdot x^{-5/2} \cdot y^{3/2}$

STEP 6

Identify $a$ , $b$ , and $c$ from the expression $4 x^{-5/2} y^{3/2}$ :
$a = 4, \quad b = -\frac{5}{2}, \quad c = \frac{3}{2}$

STEP 7

Calculate the product of $a$ , $b$ , and $c$ :
$a \times b \times c = 4 \times \left(-\frac{5}{2}\right) \times \frac{3}{2}$
$= 4 \times -\frac{15}{4}$
$= -15$
The product of $a$ , $b$ , and $c$ is:
$\boxed{-15}$

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Questionn make on paper.) PM ractionaı
Fractions / Fractions
Fractional
Question Watch Video Show Examples
If the expression $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ is written in the form $a x^{b} y^{c}$ , then what is the product of $a, b$ and $c$ ?
Answer Attempt 1 out of 2 $\square$ Submit Answer

Studdy Solution

STEP 1

1. The given expression is $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ .
2. We need to express this in the form $a x^{b} y^{c}$ .
3. We will then find the product of $a$ , $b$ , and $c$ .

STEP 2

1. Simplify the expression under the square root.
2. Simplify the entire expression $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ .
3. Identify the values of $a$ , $b$ , and $c$ .
4. Calculate the product of $a$ , $b$ , and $c$ .

STEP 3

Simplify the expression under the square root:
$\sqrt{x y^{5}} = (x y^{5})^{1/2} = x^{1/2} y^{5/2}$

STEP 4

Substitute the simplified square root expression back into the original expression:
$4 x^{-3} y^{-1} \cdot x^{1/2} y^{5/2}$

STEP 5

Combine the powers of $x$ and $y$ :
$4 \cdot x^{-3 + 1/2} \cdot y^{-1 + 5/2}$
$= 4 \cdot x^{-5/2} \cdot y^{3/2}$

STEP 6

Identify $a$ , $b$ , and $c$ from the expression $4 x^{-5/2} y^{3/2}$ :
$a = 4, \quad b = -\frac{5}{2}, \quad c = \frac{3}{2}$

STEP 7

Calculate the product of $a$ , $b$ , and $c$ :
$a \times b \times c = 4 \times \left(-\frac{5}{2}\right) \times \frac{3}{2}$
$= 4 \times -\frac{15}{4}$
$= -15$
The product of $a$ , $b$ , and $c$ is:
$\boxed{-15}$

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Studdy Solution

STEP 1

1. The given expression is 4x−3y−1xy5 4 x^{-3} y^{-1} \sqrt{x y^{5}} 4x−3y−1xy5​.2. We need to express this in the form axbyc a x^{b} y^{c} axbyc.3. We will then find the product of a a a, b b b, and c c c.

STEP 2

1. Simplify the expression under the square root.2. Simplify the entire expression 4x−3y−1xy5 4 x^{-3} y^{-1} \sqrt{x y^{5}} 4x−3y−1xy5​.3. Identify the values of a a a, b b b, and c c c.4. Calculate the product of a a a, b b b, and c c c.

STEP 3

Simplify the expression under the square root:xy5=(xy5)1/2=x1/2y5/2 \sqrt{x y^{5}} = (x y^{5})^{1/2} = x^{1/2} y^{5/2} xy5​=(xy5)1/2=x1/2y5/2

STEP 4

Substitute the simplified square root expression back into the original expression:4x−3y−1⋅x1/2y5/2 4 x^{-3} y^{-1} \cdot x^{1/2} y^{5/2} 4x−3y−1⋅x1/2y5/2

STEP 5

Combine the powers of x x x and y y y:4⋅x−3+1/2⋅y−1+5/2 4 \cdot x^{-3 + 1/2} \cdot y^{-1 + 5/2} 4⋅x−3+1/2⋅y−1+5/2=4⋅x−5/2⋅y3/2 = 4 \cdot x^{-5/2} \cdot y^{3/2} =4⋅x−5/2⋅y3/2

STEP 6

Identify a a a, b b b, and c c c from the expression 4x−5/2y3/2 4 x^{-5/2} y^{3/2} 4x−5/2y3/2:a=4,b=−52,c=32 a = 4, \quad b = -\frac{5}{2}, \quad c = \frac{3}{2} a=4,b=−25​,c=23​

STEP 7

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1. The given expression is $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ .
2. We need to express this in the form $a x^{b} y^{c}$ .
3. We will then find the product of $a$ , $b$ , and $c$ .

1. Simplify the expression under the square root.
2. Simplify the entire expression $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ .
3. Identify the values of $a$ , $b$ , and $c$ .
4. Calculate the product of $a$ , $b$ , and $c$ .

Simplify the expression under the square root:
$\sqrt{x y^{5}} = (x y^{5})^{1/2} = x^{1/2} y^{5/2}$

Substitute the simplified square root expression back into the original expression:
$4 x^{-3} y^{-1} \cdot x^{1/2} y^{5/2}$

Combine the powers of $x$ and $y$ :
$4 \cdot x^{-3 + 1/2} \cdot y^{-1 + 5/2}$
$= 4 \cdot x^{-5/2} \cdot y^{3/2}$

Identify $a$ , $b$ , and $c$ from the expression $4 x^{-5/2} y^{3/2}$ :
$a = 4, \quad b = -\frac{5}{2}, \quad c = \frac{3}{2}$