Simplify (1/32)^x*(1/2)^(9x-5)

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

Simplify the expression.

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

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

One to any power is one.

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

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

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

Combine.

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

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

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

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

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

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

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

Subtract $5$ from $1$ .

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

One to any power is one.

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

Simplify the denominator.

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

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

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

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

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

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

Add $5 x$ and $9 x$ .

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