Solve for p 3125=(-1-18p)^(5/3)

$3125 = {(- 1 - 18 p)}^{\frac{5}{3}}$

Step 1

Rewrite the equation as ${(- 1 - 18 p)}^{\frac{5}{3}} = 3125$ .

${(- 1 - 18 p)}^{\frac{5}{3}} = 3125$

Step 2

Raise each side of the equation to the power of $\frac{3}{5}$ to eliminate the fractional exponent on the left side.

${({(- 1 - 18 p)}^{\frac{5}{3}})}^{\frac{3}{5}} = 3125^{\frac{3}{5}}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${({(- 1 - 18 p)}^{\frac{5}{3}})}^{\frac{3}{5}}$ .

Multiply the exponents in ${({(- 1 - 18 p)}^{\frac{5}{3}})}^{\frac{3}{5}}$ .

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

${(- 1 - 18 p)}^{\frac{5}{3} \cdot \frac{3}{5}} = 3125^{\frac{3}{5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(- 1 - 18 p)}^{\frac{5}{3} \cdot \frac{3}{5}} = 3125^{\frac{3}{5}}$

Rewrite the expression.

${(- 1 - 18 p)}^{\frac{1}{3} \cdot 3} = 3125^{\frac{3}{5}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 1 - 18 p)}^{\frac{1}{3} \cdot 3} = 3125^{\frac{3}{5}}$

Rewrite the expression.

${(- 1 - 18 p)}^{1} = 3125^{\frac{3}{5}}$

Simplify.

$- 1 - 18 p = 3125^{\frac{3}{5}}$

Simplify the right side.

Simplify $3125^{\frac{3}{5}}$ .

Simplify the expression.

Rewrite $3125$ as $5^{5}$ .

$- 1 - 18 p = {(5^{5})}^{\frac{3}{5}}$

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

$- 1 - 18 p = 5^{5 (\frac{3}{5})}$

Cancel the common factor of $5$ .

Cancel the common factor.

$- 1 - 18 p = 5^{5 (\frac{3}{5})}$

Rewrite the expression.

$- 1 - 18 p = 5^{3}$

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

$- 1 - 18 p = 125$

Step 4

Solve for $p$ .

Move all terms not containing $p$ to the right side of the equation.

Add $1$ to both sides of the equation.

$- 18 p = 125 + 1$

Add $125$ and $1$ .

$- 18 p = 126$

Divide each term in $- 18 p = 126$ by $- 18$ and simplify.

Divide each term in $- 18 p = 126$ by $- 18$ .

$\frac{- 18 p}{- 18} = \frac{126}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 p}{- 18} = \frac{126}{- 18}$

Divide $p$ by $1$ .

$p = \frac{126}{- 18}$

Simplify the right side.

Divide $126$ by $- 18$ .

$p = - 7$

Solve for p 3125=(-1-18p)^(5/3)

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