Precalculus Examples

${(3 y^{3})}^{4} {(4 y^{2})}^{- 3}$

Step 1

Apply the product rule to $3 y^{3}$ .

$3^{4} {(y^{3})}^{4} {(4 y^{2})}^{- 3}$

Step 2

Raise $3$ to the power of $4$ .

$81 {(y^{3})}^{4} {(4 y^{2})}^{- 3}$

Step 3

Multiply the exponents in ${(y^{3})}^{4}$ .

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Step 3.1

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

$81 y^{3 \cdot 4} {(4 y^{2})}^{- 3}$

Step 3.2

Multiply $3$ by $4$ .

$81 y^{12} {(4 y^{2})}^{- 3}$

Step 4

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

$81 y^{12} \frac{1}{{(4 y^{2})}^{3}}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the product rule to $4 y^{2}$ .

$81 y^{12} \frac{1}{4^{3} {(y^{2})}^{3}}$

Step 5.2

Raise $4$ to the power of $3$ .

$81 y^{12} \frac{1}{64 {(y^{2})}^{3}}$

Step 5.3

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 5.3.1

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

$81 y^{12} \frac{1}{64 y^{2 \cdot 3}}$

Step 5.3.2

Multiply $2$ by $3$ .

$81 y^{12} \frac{1}{64 y^{6}}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $y^{6}$ .

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Step 6.1.1

Factor $y^{6}$ out of $81 y^{12}$ .

$y^{6} (81 y^{6}) \frac{1}{64 y^{6}}$

Step 6.1.2

Factor $y^{6}$ out of $64 y^{6}$ .

$y^{6} (81 y^{6}) \frac{1}{y^{6} \cdot 64}$

Step 6.1.3

Cancel the common factor.

$y^{6} (81 y^{6}) \frac{1}{y^{6} \cdot 64}$

Step 6.1.4

Rewrite the expression.

$81 y^{6} \frac{1}{64}$

Step 6.2

Combine $81$ and $\frac{1}{64}$ .

$y^{6} \frac{81}{64}$

Step 6.3

Combine $y^{6}$ and $\frac{81}{64}$ .

$\frac{y^{6} \cdot 81}{64}$

Step 6.4

Move $81$ to the left of $y^{6}$ .

$\frac{81 y^{6}}{64}$