Basic Math Examples

400 = 0.4 z^{\frac{3}{4}}

$400 = 0.4 z^{\frac{3}{4}}$

Step 1

Rewrite the equation as

0.4 z^{\frac{3}{4}} = 400

$0.4 z^{\frac{3}{4}} = 400$ .

0.4 z^{\frac{3}{4}} = 400

$0.4 z^{\frac{3}{4}} = 400$

Step 2

Divide each term in

0.4 z^{\frac{3}{4}} = 400

$0.4 z^{\frac{3}{4}} = 400$ by

0.4

$0.4$ and simplify.

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Step 2.1

Divide each term in

0.4 z^{\frac{3}{4}} = 400

$0.4 z^{\frac{3}{4}} = 400$ by

0.4

$0.4$ .

\frac{0.4 z^{\frac{3}{4}}}{0.4} = \frac{400}{0.4}

$\frac{0.4 z^{\frac{3}{4}}}{0.4} = \frac{400}{0.4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor.

$\frac{0.4 z^{\frac{3}{4}}}{0.4} = \frac{400}{0.4}$

Step 2.2.2

Divide

$z^{\frac{3}{4}}$ by

$1$ .

$z^{\frac{3}{4}} = \frac{400}{0.4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide

$400$ by

$0.4$ .

$z^{\frac{3}{4}} = 1000$

Step 3

Raise each side of the equation to the power of

$\frac{4}{3}$ to eliminate the fractional exponent on the left side.

${(z^{\frac{3}{4}})}^{\frac{4}{3}} = 1000^{\frac{4}{3}}$

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify

${(z^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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Step 4.1.1.1

Multiply the exponents in

${(z^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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Step 4.1.1.1.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$z^{\frac{3}{4} \cdot \frac{4}{3}} = 1000^{\frac{4}{3}}$

Step 4.1.1.1.2

Cancel the common factor of

$3$ .

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Step 4.1.1.1.2.1

Cancel the common factor.

$z^{\frac{3}{4} \cdot \frac{4}{3}} = 1000^{\frac{4}{3}}$

Step 4.1.1.1.2.2

Rewrite the expression.

$z^{\frac{1}{4} \cdot 4} = 1000^{\frac{4}{3}}$

Step 4.1.1.1.3

Cancel the common factor of

$4$ .

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Step 4.1.1.1.3.1

Cancel the common factor.

$z^{\frac{1}{4} \cdot 4} = 1000^{\frac{4}{3}}$

Step 4.1.1.1.3.2

Rewrite the expression.

$z^{1} = 1000^{\frac{4}{3}}$

Step 4.1.1.2

Simplify.

$z = 1000^{\frac{4}{3}}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify

$1000^{\frac{4}{3}}$ .

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Step 4.2.1.1

Simplify the expression.

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Step 4.2.1.1.1

Rewrite

$1000$ as

$10^{3}$ .

$z = {(10^{3})}^{\frac{4}{3}}$

Step 4.2.1.1.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$z = 10^{3 (\frac{4}{3})}$

Step 4.2.1.2

Cancel the common factor of

$3$ .

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Step 4.2.1.2.1

Cancel the common factor.

$z = 10^{3 (\frac{4}{3})}$

Step 4.2.1.2.2

Rewrite the expression.

$z = 10^{4}$

Step 4.2.1.3

Raise

$10$ to the power of

$4$ .

$z = 10000$