Solve for m -54=10-(m-10)^(3/2)

$- 54 = 10 - {(m - 10)}^{\frac{3}{2}}$

Rewrite the equation as $10 - {(m - 10)}^{\frac{3}{2}} = - 54$ .

$10 - {(m - 10)}^{\frac{3}{2}} = - 54$

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

Subtract $10$ from both sides of the equation.

$- {(m - 10)}^{\frac{3}{2}} = - 54 - 10$

Subtract $10$ from $- 54$ .

$- {(m - 10)}^{\frac{3}{2}} = - 64$

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(- {(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Simplify the exponent.

Simplify the left side.

Simplify ${(- {(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Simplify the expression.

Apply the product rule to $- {(m - 10)}^{\frac{3}{2}}$ .

${(- 1)}^{\frac{2}{3}} {({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{2}{3}} {({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

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

${(- 1)}^{3 (\frac{2}{3})} {({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 1)}^{3 (\frac{2}{3})} {({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Rewrite the expression.

${(- 1)}^{2} {({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Simplify the expression.

Raise $- 1$ to the power of $2$ .

$1 {({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Multiply ${({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}}$ by $1$ .

${({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Multiply the exponents in ${({(m - 10)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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

${(m - 10)}^{\frac{3}{2} \cdot \frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(m - 10)}^{\frac{3}{2} \cdot \frac{2}{3}} = {(- 64)}^{\frac{2}{3}}$

Rewrite the expression.

${(m - 10)}^{\frac{1}{2} \cdot 2} = {(- 64)}^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(m - 10)}^{\frac{1}{2} \cdot 2} = {(- 64)}^{\frac{2}{3}}$

Rewrite the expression.

${(m - 10)}^{1} = {(- 64)}^{\frac{2}{3}}$

Simplify.

$m - 10 = {(- 64)}^{\frac{2}{3}}$

Simplify the right side.

Simplify ${(- 64)}^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $- 64$ as ${(- 4)}^{3}$ .

$m - 10 = {({(- 4)}^{3})}^{\frac{2}{3}}$

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

$m - 10 = {(- 4)}^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$m - 10 = {(- 4)}^{3 (\frac{2}{3})}$

Rewrite the expression.

$m - 10 = {(- 4)}^{2}$

Raise $- 4$ to the power of $2$ .

$m - 10 = 16$

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

Add $10$ to both sides of the equation.

$m = 16 + 10$

Add $16$ and $10$ .

$m = 26$

Solve for m -54=10-(m-10)^(3/2)

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