Write the Fraction in Simplest Form ((3s^-3)^5)/(3s^-2)

$\frac{{(3 s^{- 3})}^{5}}{3 s^{- 2}}$

Step 1

Move $s^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(3 s^{- 3})}^{5} s^{2}}{3}$

Step 2

Simplify the numerator.

Apply the product rule to $3 s^{- 3}$ .

$\frac{3^{5} {(s^{- 3})}^{5} s^{2}}{3}$

Raise $3$ to the power of $5$ .

$\frac{243 {(s^{- 3})}^{5} s^{2}}{3}$

Multiply the exponents in ${(s^{- 3})}^{5}$ .

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

$\frac{243 s^{- 3 \cdot 5} s^{2}}{3}$

Multiply $- 3$ by $5$ .

$\frac{243 s^{- 15} s^{2}}{3}$

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

$\frac{243 \frac{1}{s^{15}} s^{2}}{3}$

Combine exponents.

Combine $243$ and $\frac{1}{s^{15}}$ .

$\frac{\frac{243}{s^{15}} s^{2}}{3}$

Combine $\frac{243}{s^{15}}$ and $s^{2}$ .

$\frac{\frac{243 s^{2}}{s^{15}}}{3}$

Reduce the expression $\frac{243 s^{2}}{s^{15}}$ by cancelling the common factors.

Factor $s^{2}$ out of $243 s^{2}$ .

$\frac{\frac{s^{2} \cdot 243}{s^{15}}}{3}$

Factor $s^{2}$ out of $s^{15}$ .

$\frac{\frac{s^{2} \cdot 243}{s^{2} s^{13}}}{3}$

Cancel the common factor.

$\frac{\frac{s^{2} \cdot 243}{s^{2} s^{13}}}{3}$

Rewrite the expression.

$\frac{\frac{243}{s^{13}}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{243}{s^{13}} \cdot \frac{1}{3}$

Step 4

Combine.

$\frac{243 \cdot 1}{s^{13} \cdot 3}$

Step 5

Cancel the common factor of $243$ and $3$ .

Factor $3$ out of $243 \cdot 1$ .

$\frac{3 (81 \cdot 1)}{s^{13} \cdot 3}$

Cancel the common factors.

Factor $3$ out of $s^{13} \cdot 3$ .

$\frac{3 (81 \cdot 1)}{3 \cdot s^{13}}$

Cancel the common factor.

$\frac{3 (81 \cdot 1)}{3 \cdot s^{13}}$

Rewrite the expression.

$\frac{81 \cdot 1}{s^{13}}$

Step 6

Multiply $81$ by $1$ .

$\frac{81}{s^{13}}$

Write the Fraction in Simplest Form ((3s^-3)^5)/(3s^-2)

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