Algebra Examples

$x^{5} \cdot x^{4} = a x^{z}$

Step 1

Solve the equation for $a$ .

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Step 1.1

Rewrite the equation as $a x^{z} = x^{5} \cdot x^{4}$ .

$a x^{z} = x^{5} \cdot x^{4}$

Step 1.2

Multiply $x^{5}$ by $x^{4}$ by adding the exponents.

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Step 1.2.1

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

$a x^{z} = x^{5 + 4}$

Step 1.2.2

Add $5$ and $4$ .

$a x^{z} = x^{9}$

Step 1.3

Divide each term in $a x^{z} = x^{9}$ by $x^{z}$ and simplify.

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Step 1.3.1

Divide each term in $a x^{z} = x^{9}$ by $x^{z}$ .

$\frac{a x^{z}}{x^{z}} = \frac{x^{9}}{x^{z}}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $x^{z}$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{a x^{z}}{x^{z}} = \frac{x^{9}}{x^{z}}$

Step 1.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{x^{9}}{x^{z}}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Cancel the common factor of $x^{9}$ and $x^{z}$ .

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Step 1.3.3.1.1

Factor $x^{z}$ out of $x^{9}$ .

$a = \frac{x^{z} x^{9 - z}}{x^{z}}$

Step 1.3.3.1.2

Cancel the common factors.

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Step 1.3.3.1.2.1

Multiply by $1$ .

$a = \frac{x^{z} x^{9 - z}}{x^{z} \cdot 1}$

Step 1.3.3.1.2.2

Cancel the common factor.

$a = \frac{x^{z} x^{9 - z}}{x^{z} \cdot 1}$

Step 1.3.3.1.2.3

Rewrite the expression.

$a = \frac{x^{9 - z}}{1}$

Step 1.3.3.1.2.4

Divide $x^{9 - z}$ by $1$ .

$a = x^{9 - z}$

Step 2

Simplify the right side.

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Step 2.1

Simplify ${(a x^{z})}^{9 - z}$ .

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Step 2.1.1

Apply the product rule to $a x^{z}$ .

$a = a^{9 - z} {(x^{z})}^{9 - z}$

Step 2.1.2

Multiply the exponents in ${(x^{z})}^{9 - z}$ .

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Step 2.1.2.1

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

$a = a^{9 - z} x^{z (9 - z)}$

Step 2.1.2.2

Apply the distributive property.

$a = a^{9 - z} x^{z \cdot 9 + z (- z)}$

Step 2.1.2.3

Move $9$ to the left of $z$ .

$a = a^{9 - z} x^{9 \cdot z + z (- z)}$

Step 2.1.2.4

Rewrite using the commutative property of multiplication.

$a = a^{9 - z} x^{9 \cdot z - z \cdot z}$

Step 2.1.2.5

Multiply $z$ by $z$ by adding the exponents.

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Step 2.1.2.5.1

Move $z$ .

$a = a^{9 - z} x^{9 z - (z \cdot z)}$

Step 2.1.2.5.2

Multiply $z$ by $z$ .

$a = a^{9 - z} x^{9 z - z^{2}}$