Basic Math Examples

${(- \frac{16}{49})}^{- \frac{1}{2}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{49}{16})}^{\frac{1}{2}}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $- \frac{49}{16}$ .

${(- 1)}^{\frac{1}{2}} {(\frac{49}{16})}^{\frac{1}{2}}$

Step 2.2

Apply the product rule to $\frac{49}{16}$ .

${(- 1)}^{\frac{1}{2}} \frac{49^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 3

Rewrite ${(- 1)}^{\frac{1}{2}}$ as $\sqrt{{(- 1)}^{1}}$ .

$\sqrt{{(- 1)}^{1}} \frac{49^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 4

Evaluate the exponent.

$\sqrt{- 1} \frac{49^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 5

Rewrite $\sqrt{- 1}$ as $i$ .

$i \frac{49^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $49$ as $7^{2}$ .

$i \frac{{(7^{2})}^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 6.2

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

$i \frac{7^{2 (\frac{1}{2})}}{16^{\frac{1}{2}}}$

Step 6.3

Cancel the common factor of $2$ .

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Step 6.3.1

Cancel the common factor.

$i \frac{7^{2 (\frac{1}{2})}}{16^{\frac{1}{2}}}$

Step 6.3.2

Rewrite the expression.

$i \frac{7^{1}}{16^{\frac{1}{2}}}$

Step 6.4

Evaluate the exponent.

$i \frac{7}{16^{\frac{1}{2}}}$

Step 7

Simplify the denominator.

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Step 7.1

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

$i \frac{7}{{(4^{2})}^{\frac{1}{2}}}$

Step 7.2

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

$i \frac{7}{4^{2 (\frac{1}{2})}}$

Step 7.3

Cancel the common factor of $2$ .

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Step 7.3.1

Cancel the common factor.

$i \frac{7}{4^{2 (\frac{1}{2})}}$

Step 7.3.2

Rewrite the expression.

$i \frac{7}{4^{1}}$

Step 7.4

Evaluate the exponent.

$i \frac{7}{4}$

Step 8

Combine fractions.

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Step 8.1

Combine $i$ and $\frac{7}{4}$ .

$\frac{i \cdot 7}{4}$

Step 8.2

Move $7$ to the left of $i$ .

$\frac{7 i}{4}$