Basic Math Examples

$128^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}$

Step 1

Multiply $128^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}$ .

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Step 1.1

Rewrite $128$ as $2^{7}$ .

${(2^{7})}^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}$

Step 1.2

Multiply the exponents in ${(2^{7})}^{\frac{1}{2}}$ .

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Step 1.2.1

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

$2^{7 (\frac{1}{2})} \cdot 2^{\frac{1}{2}}$

Step 1.2.2

Combine $7$ and $\frac{1}{2}$ .

$2^{\frac{7}{2}} \cdot 2^{\frac{1}{2}}$

Step 1.3

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

$2^{\frac{7}{2} + \frac{1}{2}}$

Step 1.4

Combine the numerators over the common denominator.

$2^{\frac{7 + 1}{2}}$

Step 1.5

Add $7$ and $1$ .

$2^{\frac{8}{2}}$

Step 1.6

Cancel the common factor of $8$ and $2$ .

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Step 1.6.1

Factor $2$ out of $8$ .

$2^{\frac{2 \cdot 4}{2}}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $2$ .

$2^{\frac{2 \cdot 4}{2 (1)}}$

Step 1.6.2.2

Cancel the common factor.

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

Step 1.6.2.3

Rewrite the expression.

$2^{\frac{4}{1}}$

Step 1.6.2.4

Divide $4$ by $1$ .

$2^{4}$

Step 2

Raise $2$ to the power of $4$ .

$16$