Simplify 4b^0(6b^7)^-2

$4 b^{0} {(6 b^{7})}^{- 2}$

Step 1

Anything raised to $0$ is $1$ .

$4 \cdot 1 {(6 b^{7})}^{- 2}$

Step 2

Multiply $4$ by $1$ .

$4 {(6 b^{7})}^{- 2}$

Step 3

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

$4 \frac{1}{{(6 b^{7})}^{2}}$

Step 4

Simplify the denominator.

Apply the product rule to $6 b^{7}$ .

$4 \frac{1}{6^{2} {(b^{7})}^{2}}$

Raise $6$ to the power of $2$ .

$4 \frac{1}{36 {(b^{7})}^{2}}$

Multiply the exponents in ${(b^{7})}^{2}$ .

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

$4 \frac{1}{36 b^{7 \cdot 2}}$

Multiply $7$ by $2$ .

$4 \frac{1}{36 b^{14}}$

Step 5

Cancel the common factor of $4$ .

Factor $4$ out of $36 b^{14}$ .

$4 \frac{1}{4 (9 b^{14})}$

Cancel the common factor.

$4 \frac{1}{4 (9 b^{14})}$

Rewrite the expression.

$\frac{1}{9 b^{14}}$