Simplify (25b^6)^-1.5

${(25 b^{6})}^{- 1.5}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(25 b^{6})}^{1.5}}$

Step 2

Simplify the denominator.

Apply the product rule to $25 b^{6}$ .

$\frac{1}{25^{1.5} {(b^{6})}^{1.5}}$

Raise $25$ to the power of $1.5$ .

$\frac{1}{125 {(b^{6})}^{1.5}}$

Multiply the exponents in ${(b^{6})}^{1.5}$ .

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

$\frac{1}{125 b^{6 \cdot 1.5}}$

Multiply $6$ by $1.5$ .

$\frac{1}{125 b^{9}}$

Step 3

Simplify with factoring out.

Rewrite $1$ as $1 (1)$ .

$\frac{1 (1)}{125 b^{9}}$

Factor $125$ out of $125 b^{9}$ .

$\frac{1 (1)}{125 (b^{9})}$

Step 4

Separate fractions.

$\frac{1}{125} \cdot \frac{1}{b^{9}}$

Step 5

Divide $1$ by $125$ .

$0.008 \frac{1}{b^{9}}$

Step 6

Combine $0.008$ and $\frac{1}{b^{9}}$ .

$\frac{0.008}{b^{9}}$