Write the Fraction in Simplest Form ((2p^3k^-3)^-5)/(10k^-6)

$\frac{{(2 p^{3} k^{- 3})}^{- 5}}{10 k^{- 6}}$

Step 1

Move ${(2 p^{3} k^{- 3})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{10 k^{- 6} {(2 p^{3} k^{- 3})}^{5}}$

Step 2

Move $k^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{k^{6}}{10 {(2 p^{3} k^{- 3})}^{5}}$

Step 3

Simplify the denominator.

Apply the product rule to $2 p^{3} k^{- 3}$ .

$\frac{k^{6}}{10 {(2 p^{3})}^{5} {(k^{- 3})}^{5}}$

Apply the product rule to $2 p^{3}$ .

$\frac{k^{6}}{10 (2^{5} {(p^{3})}^{5}) {(k^{- 3})}^{5}}$

Raise $2$ to the power of $5$ .

$\frac{k^{6}}{10 (32 {(p^{3})}^{5}) {(k^{- 3})}^{5}}$

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

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

$\frac{k^{6}}{10 (32 p^{3 \cdot 5}) {(k^{- 3})}^{5}}$

Multiply $3$ by $5$ .

$\frac{k^{6}}{10 (32 p^{15}) {(k^{- 3})}^{5}}$

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

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

$\frac{k^{6}}{10 (32 p^{15}) k^{- 3 \cdot 5}}$

Multiply $- 3$ by $5$ .

$\frac{k^{6}}{10 (32 p^{15}) k^{- 15}}$

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

$\frac{k^{6}}{10 \cdot 32 p^{15} \frac{1}{k^{15}}}$

Combine exponents.

Multiply $10$ by $32$ .

$\frac{k^{6}}{320 p^{15} \frac{1}{k^{15}}}$

Combine $320$ and $\frac{1}{k^{15}}$ .

$\frac{k^{6}}{p^{15} \frac{320}{k^{15}}}$

Combine $p^{15}$ and $\frac{320}{k^{15}}$ .

$\frac{k^{6}}{\frac{p^{15} \cdot 320}{k^{15}}}$

Move $320$ to the left of $p^{15}$ .

$\frac{k^{6}}{\frac{320 p^{15}}{k^{15}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$k^{6} \frac{k^{15}}{320 p^{15}}$

Step 5

Multiply $k^{6} \frac{k^{15}}{320 p^{15}}$ .

Combine $k^{6}$ and $\frac{k^{15}}{320 p^{15}}$ .

$\frac{k^{6} k^{15}}{320 p^{15}}$

Multiply $k^{6}$ by $k^{15}$ by adding the exponents.

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

$\frac{k^{6 + 15}}{320 p^{15}}$

Add $6$ and $15$ .

$\frac{k^{21}}{320 p^{15}}$

Write the Fraction in Simplest Form ((2p^3k^-3)^-5)/(10k^-6)

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