Algebra Examples

${(4^{2})}^{\frac{1}{2}} {(5 x^{2})}^{3}$

Step 1

Multiply the exponents in ${(4^{2})}^{\frac{1}{2}}$ .

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Step 1.1

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

$4^{2 (\frac{1}{2})} {(5 x^{2})}^{3}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

$4^{2 (\frac{1}{2})} {(5 x^{2})}^{3}$

Step 1.2.2

Rewrite the expression.

$4^{1} {(5 x^{2})}^{3}$

Step 2

Evaluate the exponent.

$4 {(5 x^{2})}^{3}$

Step 3

Apply the product rule to $5 x^{2}$ .

$4 (5^{3} {(x^{2})}^{3})$

Step 4

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

$4 (125 {(x^{2})}^{3})$

Step 5

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 5.1

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

$4 (125 x^{2 \cdot 3})$

Step 5.2

Multiply $2$ by $3$ .

$4 (125 x^{6})$

Step 6

Multiply $125$ by $4$ .

$500 x^{6}$