Write the Fraction in Simplest Form (4y^6c^10)/((2y^4c)^-1)

$\frac{4 y^{6} c^{10}}{{(2 y^{4} c)}^{- 1}}$

Step 1

Move ${(2 y^{4} c)}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4 y^{6} c^{10} (2 y^{4} c)$

Step 2

Multiply $y^{6}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$4 (y^{4} y^{6}) c^{10} (2 c)$

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

$4 y^{4 + 6} c^{10} (2 c)$

Add $4$ and $6$ .

$4 y^{10} c^{10} (2 c)$

Step 3

Multiply $c^{10}$ by $c$ by adding the exponents.

Move $c$ .

$4 y^{10} (c \cdot c^{10}) \cdot 2$

Multiply $c$ by $c^{10}$ .

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

$4 y^{10} (c^{1} c^{10}) \cdot 2$

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

$4 y^{10} c^{1 + 10} \cdot 2$

Add $1$ and $10$ .

$4 y^{10} c^{11} \cdot 2$

Step 4

Multiply $2$ by $4$ .

$8 y^{10} c^{11}$