Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{4}{y}$ .

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

Step 1.2

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

$\frac{64}{y^{3}} {(\frac{3}{y})}^{4}$

Step 1.3

Apply the product rule to $\frac{3}{y}$ .

$\frac{64}{y^{3}} \cdot \frac{3^{4}}{y^{4}}$

Step 2

Combine.

$\frac{64 \cdot 3^{4}}{y^{3} y^{4}}$

Step 3

Multiply $y^{3}$ by $y^{4}$ by adding the exponents.

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Step 3.1

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

$\frac{64 \cdot 3^{4}}{y^{3 + 4}}$

Step 3.2

Add $3$ and $4$ .

$\frac{64 \cdot 3^{4}}{y^{7}}$

Step 4

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

$\frac{64 \cdot 81}{y^{7}}$

Step 5

Multiply $64$ by $81$ .

$\frac{5184}{y^{7}}$