Simplify (3y^6)/(4(y^-1)^3)

$\frac{3 y^{6}}{4 {(y^{- 1})}^{3}}$

Step 1

Simplify the denominator.

Multiply the exponents in ${(y^{- 1})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3 y^{6}}{4 y^{- 1 \cdot 3}}$

Multiply $- 1$ by $3$ .

$\frac{3 y^{6}}{4 y^{- 3}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 y^{6}}{4 \frac{1}{y^{3}}}$

Step 2

Combine $4$ and $\frac{1}{y^{3}}$ .

$\frac{3 y^{6}}{\frac{4}{y^{3}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$3 y^{6} \frac{y^{3}}{4}$

Step 4

Multiply $3 y^{6} \frac{y^{3}}{4}$ .

Combine $3$ and $\frac{y^{3}}{4}$ .

$y^{6} \frac{3 y^{3}}{4}$

Combine $y^{6}$ and $\frac{3 y^{3}}{4}$ .

$\frac{y^{6} (3 y^{3})}{4}$

Multiply $y^{6}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$\frac{y^{3} y^{6} \cdot 3}{4}$

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

$\frac{y^{3 + 6} \cdot 3}{4}$

Add $3$ and $6$ .

$\frac{y^{9} \cdot 3}{4}$

Step 5

Move $3$ to the left of $y^{9}$ .

$\frac{3 y^{9}}{4}$