Algebra Examples

${(\frac{2 r^{3} t^{6}}{5 u^{9}})}^{4}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $\frac{2 r^{3} t^{6}}{5 u^{9}}$ .

$\frac{{(2 r^{3} t^{6})}^{4}}{{(5 u^{9})}^{4}}$

Step 1.2

Apply the product rule to $2 r^{3} t^{6}$ .

$\frac{{(2 r^{3})}^{4} {(t^{6})}^{4}}{{(5 u^{9})}^{4}}$

Step 1.3

Apply the product rule to $2 r^{3}$ .

$\frac{2^{4} {(r^{3})}^{4} {(t^{6})}^{4}}{{(5 u^{9})}^{4}}$

Step 1.4

Apply the product rule to $5 u^{9}$ .

$\frac{2^{4} {(r^{3})}^{4} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $2$ to the power of $4$ .

$\frac{16 {(r^{3})}^{4} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{16 r^{3 \cdot 4} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

Step 2.2.2

Multiply $3$ by $4$ .

$\frac{16 r^{12} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

Step 2.3

Multiply the exponents in ${(t^{6})}^{4}$ .

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Step 2.3.1

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

$\frac{16 r^{12} t^{6 \cdot 4}}{5^{4} {(u^{9})}^{4}}$

Step 2.3.2

Multiply $6$ by $4$ .

$\frac{16 r^{12} t^{24}}{5^{4} {(u^{9})}^{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $5$ to the power of $4$ .

$\frac{16 r^{12} t^{24}}{625 {(u^{9})}^{4}}$

Step 3.2

Multiply the exponents in ${(u^{9})}^{4}$ .

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Step 3.2.1

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

$\frac{16 r^{12} t^{24}}{625 u^{9 \cdot 4}}$

Step 3.2.2

Multiply $9$ by $4$ .

$\frac{16 r^{12} t^{24}}{625 u^{36}}$