Pre-Algebra Examples

 $\begin{array}{r} h = & H h \\ l = & g h \\ w = & g h \end{array}$

Step 1

The volume of a box is equal to the length $l$ times the width $w$ times the height $h$ .

$(l e n g t h) \cdot (w i d t h) \cdot (h e i g h t)$

Step 2

Substitute the values of the length $l = g h$ , the width $w = g h$ , and the height $h = H h$ into the formula.

$g h \cdot (g h) \cdot (H h)$

Step 3

Multiply $g$ by $g$ by adding the exponents.

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Step 3.1

Move $g$ .

$g \cdot g h \cdot h \cdot (H h)$

Step 3.2

Multiply $g$ by $g$ .

$g^{2} h \cdot h \cdot (H h)$

Step 4

Multiply $h$ by $h$ by adding the exponents.

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Step 4.1

Move $h$ .

$g^{2} (h \cdot h) \cdot (H h)$

Step 4.2

Multiply $h$ by $h$ .

$g^{2} h^{2} \cdot (H h)$

Step 5

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

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Step 5.1

Move $h$ .

$g^{2} (h \cdot h^{2}) \cdot H$

Step 5.2

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

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Step 5.2.1

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

$g^{2} (h^{1} h^{2}) \cdot H$

Step 5.2.2

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

$g^{2} h^{1 + 2} \cdot H$

Step 5.3

Add $1$ and $2$ .

$g^{2} h^{3} \cdot H$

$g^{2} h^{3} H$