Algebra Examples

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

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

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to

\frac{4}{y}

$\frac{4}{y}$ .

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

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

Step 1.2

Raise

4

$4$ to the power of

3

$3$ .

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

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

Step 1.3

Apply the product rule to

\frac{3}{y}

$\frac{3}{y}$ .

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

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

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

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

Step 2

Combine.

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

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

Step 3

Multiply

y^{3}

$y^{3}$ by

y^{4}

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

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Step 3.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 3.2

Add

3

$3$ and

4

$4$ .

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

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

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

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

Step 4

Raise

3

$3$ to the power of

4

$4$ .

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

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

Step 5

Multiply

64

$64$ by

81

$81$ .

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

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

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

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

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$