Basic Math Examples

$Q = 30 {(10000)}^{\frac{1}{4}} {(2401)}^{\frac{3}{4}}$

Step 1

Remove parentheses.

$Q = 30 \cdot (10000^{\frac{1}{4}} {(2401)}^{\frac{3}{4}})$

Step 2

Remove parentheses.

$Q = 30 \cdot 10000^{\frac{1}{4}} \cdot 2401^{\frac{3}{4}}$

Step 3

Simplify $30 \cdot 10000^{\frac{1}{4}} \cdot 2401^{\frac{3}{4}}$ .

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Step 3.1

Simplify the expression.

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Step 3.1.1

Rewrite $10000$ as $10^{4}$ .

$Q = 30 \cdot {(10^{4})}^{\frac{1}{4}} \cdot 2401^{\frac{3}{4}}$

Step 3.1.2

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

$Q = 30 \cdot 10^{4 (\frac{1}{4})} \cdot 2401^{\frac{3}{4}}$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Cancel the common factor.

$Q = 30 \cdot 10^{4 (\frac{1}{4})} \cdot 2401^{\frac{3}{4}}$

Step 3.2.2

Rewrite the expression.

$Q = 30 \cdot 10^{1} \cdot 2401^{\frac{3}{4}}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Evaluate the exponent.

$Q = 30 \cdot 10 \cdot 2401^{\frac{3}{4}}$

Step 3.3.2

Multiply $30$ by $10$ .

$Q = 300 \cdot 2401^{\frac{3}{4}}$

Step 3.3.3

Rewrite $2401$ as $7^{4}$ .

$Q = 300 \cdot {(7^{4})}^{\frac{3}{4}}$

Step 3.3.4

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

$Q = 300 \cdot 7^{4 (\frac{3}{4})}$

Step 3.4

Cancel the common factor of $4$ .

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Step 3.4.1

Cancel the common factor.

$Q = 300 \cdot 7^{4 (\frac{3}{4})}$

Step 3.4.2

Rewrite the expression.

$Q = 300 \cdot 7^{3}$

Step 3.5

Simplify the expression.

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Step 3.5.1

Raise $7$ to the power of $3$ .

$Q = 300 \cdot 343$

Step 3.5.2

Multiply $300$ by $343$ .

$Q = 102900$