Algebra Examples

$(h^{2}) (h^{10}) = {(h^{2})}^{x^{2} + 5 x + 6}$

Step 1

Rewrite the equation as ${(h^{2})}^{x^{2} + 5 x + 6} = h^{2} (h^{10})$ .

${(h^{2})}^{x^{2} + 5 x + 6} = h^{2} (h^{10})$

Step 2

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

$h^{2 (x^{2} + 5 x + 6)} = h^{2} (h^{10})$

Step 3

Multiply $h^{2}$ by $h^{10}$ by adding the exponents.

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Step 3.1

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

$h^{2 (x^{2} + 5 x + 6)} = h^{2 + 10}$

Step 3.2

Add $2$ and $10$ .

$h^{2 (x^{2} + 5 x + 6)} = h^{12}$

Step 4

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 (x^{2} + 5 x + 6) = 12$

Step 5

Solve for $x$ .

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Step 5.1

Divide each term in $2 (x^{2} + 5 x + 6) = 12$ by $2$ and simplify.

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Step 5.1.1

Divide each term in $2 (x^{2} + 5 x + 6) = 12$ by $2$ .

$\frac{2 (x^{2} + 5 x + 6)}{2} = \frac{12}{2}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $2$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{2 (x^{2} + 5 x + 6)}{2} = \frac{12}{2}$

Step 5.1.2.1.2

Divide $x^{2} + 5 x + 6$ by $1$ .

$x^{2} + 5 x + 6 = \frac{12}{2}$

Step 5.1.3

Simplify the right side.

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Step 5.1.3.1

Divide $12$ by $2$ .

$x^{2} + 5 x + 6 = 6$

Step 5.2

Subtract $6$ from both sides of the equation.

$x^{2} + 5 x + 6 - 6 = 0$

Step 5.3

Combine the opposite terms in $x^{2} + 5 x + 6 - 6$ .

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Step 5.3.1

Subtract $6$ from $6$ .

$x^{2} + 5 x + 0 = 0$

Step 5.3.2

Add $x^{2} + 5 x$ and $0$ .

$x^{2} + 5 x = 0$

Step 5.4

Factor $x$ out of $x^{2} + 5 x$ .

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Step 5.4.1

Factor $x$ out of $x^{2}$ .

$x \cdot x + 5 x = 0$

Step 5.4.2

Factor $x$ out of $5 x$ .

$x \cdot x + x \cdot 5 = 0$

Step 5.4.3

Factor $x$ out of $x \cdot x + x \cdot 5$ .

$x (x + 5) = 0$

Step 5.5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 5 = 0$

Step 5.6

Set $x$ equal to $0$ .

$x = 0$

Step 5.7

Set $x + 5$ equal to $0$ and solve for $x$ .

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Step 5.7.1

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Step 5.7.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 5.8

The final solution is all the values that make $x (x + 5) = 0$ true.

$x = 0, - 5$