Algebra Examples

${(\frac{1}{32})}^{x} \cdot {(\frac{1}{2})}^{9 x - 5}$

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{1}{32}$ .

$\frac{1^{x}}{32^{x}} \cdot {(\frac{1}{2})}^{9 x - 5}$

Step 1.2

One to any power is one.

$\frac{1}{32^{x}} \cdot {(\frac{1}{2})}^{9 x - 5}$

Step 1.3

Apply the product rule to $\frac{1}{2}$ .

$\frac{1}{32^{x}} \cdot \frac{1^{9 x - 5}}{2^{9 x - 5}}$

Step 2

Combine.

$\frac{1 \cdot 1^{9 x - 5}}{32^{x} \cdot 2^{9 x - 5}}$

Step 3

Multiply $1$ by $1^{9 x - 5}$ by adding the exponents.

Tap for more steps...

Step 3.1

Multiply $1$ by $1^{9 x - 5}$ .

Tap for more steps...

Step 3.1.1

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

$\frac{1^{1} \cdot 1^{9 x - 5}}{32^{x} \cdot 2^{9 x - 5}}$

Step 3.1.2

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

$\frac{1^{1 + 9 x - 5}}{32^{x} \cdot 2^{9 x - 5}}$

Step 3.2

Subtract $5$ from $1$ .

$\frac{1^{9 x - 4}}{32^{x} \cdot 2^{9 x - 5}}$

Step 4

One to any power is one.

$\frac{1}{32^{x} \cdot 2^{9 x - 5}}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Rewrite $32$ as $2^{5}$ .

$\frac{1}{{(2^{5})}^{x} \cdot 2^{9 x - 5}}$

Step 5.2

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

$\frac{1}{2^{5 x} \cdot 2^{9 x - 5}}$

Step 5.3

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

$\frac{1}{2^{5 x + 9 x - 5}}$

Step 5.4

Add $5 x$ and $9 x$ .

$\frac{1}{2^{14 x - 5}}$