Basic Math Examples

${(s^{2 + t^{3}})}^{4} \cdot {(\frac{s^{2}}{t^{3}})}^{3} \div {(\frac{s}{t})}^{5}$

Step 1

Rewrite the division as a fraction.

$\frac{{(s^{2 + t^{3}})}^{4} \cdot {(\frac{s^{2}}{t^{3}})}^{3}}{{(\frac{s}{t})}^{5}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{s^{2}}{t^{3}}$ .

$\frac{{(s^{2 + t^{3}})}^{4} \frac{{(s^{2})}^{3}}{{(t^{3})}^{3}}}{{(\frac{s}{t})}^{5}}$

Step 2.2

Multiply the exponents in ${(s^{2 + t^{3}})}^{4}$ .

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Step 2.2.1

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

$\frac{s^{(2 + t^{3}) \cdot 4} \frac{{(s^{2})}^{3}}{{(t^{3})}^{3}}}{{(\frac{s}{t})}^{5}}$

Step 2.2.2

Apply the distributive property.

$\frac{s^{2 \cdot 4 + t^{3} \cdot 4} \frac{{(s^{2})}^{3}}{{(t^{3})}^{3}}}{{(\frac{s}{t})}^{5}}$

Step 2.2.3

Multiply $2$ by $4$ .

$\frac{s^{8 + t^{3} \cdot 4} \frac{{(s^{2})}^{3}}{{(t^{3})}^{3}}}{{(\frac{s}{t})}^{5}}$

Step 2.2.4

Move $4$ to the left of $t^{3}$ .

$\frac{s^{8 + 4 t^{3}} \frac{{(s^{2})}^{3}}{{(t^{3})}^{3}}}{{(\frac{s}{t})}^{5}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{s^{8 + 4 t^{3}} \frac{s^{2 \cdot 3}}{{(t^{3})}^{3}}}{{(\frac{s}{t})}^{5}}$

Step 2.3.2

Multiply $2$ by $3$ .

$\frac{s^{8 + 4 t^{3}} \frac{s^{6}}{{(t^{3})}^{3}}}{{(\frac{s}{t})}^{5}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{s^{8 + 4 t^{3}} \frac{s^{6}}{t^{3 \cdot 3}}}{{(\frac{s}{t})}^{5}}$

Step 2.4.2

Multiply $3$ by $3$ .

$\frac{s^{8 + 4 t^{3}} \frac{s^{6}}{t^{9}}}{{(\frac{s}{t})}^{5}}$

Step 3

Combine fractions.

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Step 3.1

Apply the product rule to $\frac{s}{t}$ .

$\frac{s^{8 + 4 t^{3}} \frac{s^{6}}{t^{9}}}{\frac{s^{5}}{t^{5}}}$

Step 3.2

Combine $s^{8 + 4 t^{3}}$ and $\frac{s^{6}}{t^{9}}$ .

$\frac{\frac{s^{8 + 4 t^{3}} s^{6}}{t^{9}}}{\frac{s^{5}}{t^{5}}}$

Step 4

Multiply $s^{8 + 4 t^{3}}$ by $s^{6}$ by adding the exponents.

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Step 4.1

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

$\frac{\frac{s^{8 + 4 t^{3} + 6}}{t^{9}}}{\frac{s^{5}}{t^{5}}}$

Step 4.2

Add $8$ and $6$ .

$\frac{\frac{s^{4 t^{3} + 14}}{t^{9}}}{\frac{s^{5}}{t^{5}}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{s^{4 t^{3} + 14}}{t^{9}} \cdot \frac{t^{5}}{s^{5}}$

Step 6

Combine.

$\frac{s^{4 t^{3} + 14} t^{5}}{t^{9} s^{5}}$

Step 7

Cancel the common factor of $s^{4 t^{3} + 14}$ and $s^{5}$ .

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Step 7.1

Factor $s^{5}$ out of $s^{4 t^{3} + 14} t^{5}$ .

$\frac{s^{5} (s^{4 t^{3} + 9} t^{5})}{t^{9} s^{5}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $s^{5}$ out of $t^{9} s^{5}$ .

$\frac{s^{5} (s^{4 t^{3} + 9} t^{5})}{s^{5} t^{9}}$

Step 7.2.2

Cancel the common factor.

$\frac{s^{5} (s^{4 t^{3} + 9} t^{5})}{s^{5} t^{9}}$

Step 7.2.3

Rewrite the expression.

$\frac{s^{4 t^{3} + 9} t^{5}}{t^{9}}$

Step 8

Cancel the common factor of $t^{5}$ and $t^{9}$ .

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Step 8.1

Factor $t^{5}$ out of $s^{4 t^{3} + 9} t^{5}$ .

$\frac{t^{5} s^{4 t^{3} + 9}}{t^{9}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $t^{5}$ out of $t^{9}$ .

$\frac{t^{5} s^{4 t^{3} + 9}}{t^{5} t^{4}}$

Step 8.2.2

Cancel the common factor.

$\frac{t^{5} s^{4 t^{3} + 9}}{t^{5} t^{4}}$

Step 8.2.3

Rewrite the expression.

$\frac{s^{4 t^{3} + 9}}{t^{4}}$