Precalculus Examples

${(s^{- 2} t^{2})}^{2} {(s^{2} t)}^{3}$

Step 1

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

${(\frac{1}{s^{2}} t^{2})}^{2} {(s^{2} t)}^{3}$

Step 2

Combine $\frac{1}{s^{2}}$ and $t^{2}$ .

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

Step 3

Apply basic rules of exponents.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $2$ by $2$ .

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

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

Step 3.4

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

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

Step 3.5

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

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Step 3.5.1

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

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

Step 3.5.2

Multiply $2$ by $3$ .

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

Step 4

Cancel the common factor of $s^{4}$ .

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Step 4.1

Factor $s^{4}$ out of $s^{6} t^{3}$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$t^{4} (s^{2} t^{3})$

Step 5

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

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Step 5.1

Move $t^{3}$ .

$t^{3} t^{4} s^{2}$

Step 5.2

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

$t^{3 + 4} s^{2}$

Step 5.3

Add $3$ and $4$ .

$t^{7} s^{2}$