Pre-Algebra Examples

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

Step 1

Move $t^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $t$ by $t^{2}$ by adding the exponents.

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Step 2.1

Move $t^{2}$ .

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

Step 2.2

Multiply $t^{2}$ by $t$ .

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Step 2.2.1

Raise $t$ to the power of $1$ .

${(\frac{3 a^{4}}{a^{2} (t^{2} t^{1})})}^{4}$

Step 2.2.2

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

${(\frac{3 a^{4}}{a^{2} t^{2 + 1}})}^{4}$

Step 2.3

Add $2$ and $1$ .

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

Step 3

Cancel the common factor of $a^{4}$ and $a^{2}$ .

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Step 3.1

Factor $a^{2}$ out of $3 a^{4}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{2}$ out of $a^{2} t^{3}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Simplify the numerator.

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Step 5.1

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

$\frac{81 {(a^{2})}^{4}}{{(t^{3})}^{4}}$

Step 5.2

Multiply the exponents in ${(a^{2})}^{4}$ .

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Step 5.2.1

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

$\frac{81 a^{2 \cdot 4}}{{(t^{3})}^{4}}$

Step 5.2.2

Multiply $2$ by $4$ .

$\frac{81 a^{8}}{{(t^{3})}^{4}}$

Step 6

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

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Step 6.1

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

$\frac{81 a^{8}}{t^{3 \cdot 4}}$

Step 6.2

Multiply $3$ by $4$ .

$\frac{81 a^{8}}{t^{12}}$