Basic Math Examples

${(z - 1)}^{\frac{3}{5}} = 2$

Step 1

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

${({(z - 1)}^{\frac{3}{5}})}^{\frac{5}{3}} = 2^{\frac{5}{3}}$

Step 2

Simplify the left side.

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Step 2.1

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

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Step 2.1.1

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

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Step 2.1.1.1

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

${(z - 1)}^{\frac{3}{5} \cdot \frac{5}{3}} = 2^{\frac{5}{3}}$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

${(z - 1)}^{\frac{3}{5} \cdot \frac{5}{3}} = 2^{\frac{5}{3}}$

Step 2.1.1.2.2

Rewrite the expression.

${(z - 1)}^{\frac{1}{5} \cdot 5} = 2^{\frac{5}{3}}$

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Cancel the common factor.

${(z - 1)}^{\frac{1}{5} \cdot 5} = 2^{\frac{5}{3}}$

Step 2.1.1.3.2

Rewrite the expression.

${(z - 1)}^{1} = 2^{\frac{5}{3}}$

Step 2.1.2

Simplify.

$z - 1 = 2^{\frac{5}{3}}$

Step 3

Add $1$ to both sides of the equation.

$z = 2^{\frac{5}{3}} + 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = 2^{\frac{5}{3}} + 1$

Decimal Form:

$z = 4.17480210 \dots$