Simplify (3a^-2)^3*3a^5

${(3 a^{- 2})}^{3} \cdot 3 a^{5}$

Step 1

Rewrite using the commutative property of multiplication.

$3 {(3 a^{- 2})}^{3} a^{5}$

Step 2

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

$3 {(3 \frac{1}{a^{2}})}^{3} a^{5}$

Step 3

Combine $3$ and $\frac{1}{a^{2}}$ .

$3 {(\frac{3}{a^{2}})}^{3} a^{5}$

Step 4

Simplify the expression.

Apply the product rule to $\frac{3}{a^{2}}$ .

$3 \frac{3^{3}}{{(a^{2})}^{3}} a^{5}$

Raise $3$ to the power of $3$ .

$3 \frac{27}{{(a^{2})}^{3}} a^{5}$

Multiply the exponents in ${(a^{2})}^{3}$ .

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

$3 \frac{27}{a^{2 \cdot 3}} a^{5}$

Multiply $2$ by $3$ .

$3 \frac{27}{a^{6}} a^{5}$

Step 5

Multiply $3 \frac{27}{a^{6}}$ .

Combine $3$ and $\frac{27}{a^{6}}$ .

$\frac{3 \cdot 27}{a^{6}} a^{5}$

Multiply $3$ by $27$ .

$\frac{81}{a^{6}} a^{5}$

Step 6

Cancel the common factor of $a^{5}$ .

Factor $a^{5}$ out of $a^{6}$ .

$\frac{81}{a^{5} a} a^{5}$

Cancel the common factor.

$\frac{81}{a^{5} a} a^{5}$

Rewrite the expression.

$\frac{81}{a}$