Pre-Algebra Examples

$(3 t) {(3 t)}^{5}$

Step 1

Apply the product rule to $3 t$ .

$3 t (3^{5} t^{5})$

Step 2

Rewrite using the commutative property of multiplication.

$3 \cdot 3^{5} t \cdot t^{5}$

Step 3

Multiply $3$ by $3^{5}$ by adding the exponents.

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Step 3.1

Multiply $3$ by $3^{5}$ .

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Step 3.1.1

Raise $3$ to the power of $1$ .

$3^{1} \cdot 3^{5} t \cdot t^{5}$

Step 3.1.2

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

$3^{1 + 5} t \cdot t^{5}$

Step 3.2

Add $1$ and $5$ .

$3^{6} t \cdot t^{5}$

Step 4

Multiply $t$ by $t^{5}$ by adding the exponents.

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Step 4.1

Move $t^{5}$ .

$3^{6} (t^{5} t)$

Step 4.2

Multiply $t^{5}$ by $t$ .

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Step 4.2.1

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

$3^{6} (t^{5} t^{1})$

Step 4.2.2

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

$3^{6} t^{5 + 1}$

Step 4.3

Add $5$ and $1$ .

$3^{6} t^{6}$

Step 5

Raise $3$ to the power of $6$ .

$729 t^{6}$