Algebra Examples

${(x^{5})}^{3} {(16 x^{8})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

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Step 1.1

Multiply the exponents in ${(x^{5})}^{3}$ .

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Step 1.1.1

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

$x^{5 \cdot 3} {(16 x^{8})}^{\frac{1}{2}}$

Step 1.1.2

Multiply $5$ by $3$ .

$x^{15} {(16 x^{8})}^{\frac{1}{2}}$

Step 1.2

Apply the product rule to $16 x^{8}$ .

$x^{15} (16^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}})$

Step 1.3

Rewrite using the commutative property of multiplication.

$16^{\frac{1}{2}} x^{15} {(x^{8})}^{\frac{1}{2}}$

Step 1.4

Rewrite $16$ as $4^{2}$ .

${(4^{2})}^{\frac{1}{2}} x^{15} {(x^{8})}^{\frac{1}{2}}$

Step 1.5

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

$4^{2 (\frac{1}{2})} x^{15} {(x^{8})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$4^{2 (\frac{1}{2})} x^{15} {(x^{8})}^{\frac{1}{2}}$

Step 2.2

Rewrite the expression.

$4^{1} x^{15} {(x^{8})}^{\frac{1}{2}}$

Step 3

Simplify the expression.

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Step 3.1

Evaluate the exponent.

$4 x^{15} {(x^{8})}^{\frac{1}{2}}$

Step 3.2

Multiply the exponents in ${(x^{8})}^{\frac{1}{2}}$ .

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Step 3.2.1

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

$4 x^{15} x^{8 (\frac{1}{2})}$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $8$ .

$4 x^{15} x^{2 (4) \frac{1}{2}}$

Step 3.2.2.2

Cancel the common factor.

$4 x^{15} x^{2 \cdot 4 \frac{1}{2}}$

Step 3.2.2.3

Rewrite the expression.

$4 x^{15} x^{4}$

Step 4

Multiply $x^{15}$ by $x^{4}$ by adding the exponents.

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Step 4.1

Move $x^{4}$ .

$4 (x^{4} x^{15})$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{4 + 15}$

Step 4.3

Add $4$ and $15$ .

$4 x^{19}$