Simplify (6x^-1y^(7/2))/( square root of 16x^2y^2)

$\frac{6 x^{- 1} y^{\frac{7}{2}}}{\sqrt{16 x^{2} y^{2}}}$

Step 1

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{6 y^{\frac{7}{2}}}{\sqrt{16 x^{2} y^{2}} x}$

Step 2

Simplify the denominator.

Rewrite $16 x^{2} y^{2}$ as ${(4 x y)}^{2}$ .

$\frac{6 y^{\frac{7}{2}}}{\sqrt{{(4 x y)}^{2}} x}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{6 y^{\frac{7}{2}}}{4 x y x}$

Combine exponents.

Raise $x$ to the power of $1$ .

$\frac{6 y^{\frac{7}{2}}}{4 (x^{1} x) y}$

Raise $x$ to the power of $1$ .

$\frac{6 y^{\frac{7}{2}}}{4 (x^{1} x^{1}) y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 y^{\frac{7}{2}}}{4 x^{1 + 1} y}$

Add $1$ and $1$ .

$\frac{6 y^{\frac{7}{2}}}{4 x^{2} y}$

Step 3

Move $y^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{6 y^{\frac{7}{2}} y^{- 1}}{4 x^{2}}$

Step 4

Multiply $y^{\frac{7}{2}}$ by $y^{- 1}$ by adding the exponents.

Move $y^{- 1}$ .

$\frac{6 (y^{- 1} y^{\frac{7}{2}})}{4 x^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 y^{- 1 + \frac{7}{2}}}{4 x^{2}}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 y^{- 1 \cdot \frac{2}{2} + \frac{7}{2}}}{4 x^{2}}$

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{6 y^{\frac{- 1 \cdot 2}{2} + \frac{7}{2}}}{4 x^{2}}$

Combine the numerators over the common denominator.

$\frac{6 y^{\frac{- 1 \cdot 2 + 7}{2}}}{4 x^{2}}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{6 y^{\frac{- 2 + 7}{2}}}{4 x^{2}}$

Add $- 2$ and $7$ .

$\frac{6 y^{\frac{5}{2}}}{4 x^{2}}$

Step 5

Factor $2$ out of $6 y^{\frac{5}{2}}$ .

$\frac{2 (3 y^{\frac{5}{2}})}{4 x^{2}}$

Step 6

Cancel the common factors.

Factor $2$ out of $4 x^{2}$ .

$\frac{2 (3 y^{\frac{5}{2}})}{2 (2 x^{2})}$

Cancel the common factor.

$\frac{2 (3 y^{\frac{5}{2}})}{2 (2 x^{2})}$

Rewrite the expression.

$\frac{3 y^{\frac{5}{2}}}{2 x^{2}}$

Simplify (6x^-1y^(7/2))/( square root of 16x^2y^2)

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