Basic Math Examples

$\sqrt{\frac{16}{a^{2}}} = \frac{32}{a}$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{16}{a^{2}}}}^{2} = {(\frac{32}{a})}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{16}{a^{2}}}$ as ${(\frac{16}{a^{2}})}^{\frac{1}{2}}$ .

${({(\frac{16}{a^{2}})}^{\frac{1}{2}})}^{2} = {(\frac{32}{a})}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(\frac{16}{a^{2}})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(\frac{16}{a^{2}})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(\frac{16}{a^{2}})}^{\frac{1}{2} \cdot 2} = {(\frac{32}{a})}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(\frac{16}{a^{2}})}^{\frac{1}{2} \cdot 2} = {(\frac{32}{a})}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(\frac{16}{a^{2}})}^{1} = {(\frac{32}{a})}^{2}$

Step 2.2.1.2

Simplify.

$\frac{16}{a^{2}} = {(\frac{32}{a})}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify ${(\frac{32}{a})}^{2}$ .

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Step 2.3.1.1

Apply the product rule to $\frac{32}{a}$ .

$\frac{16}{a^{2}} = \frac{32^{2}}{a^{2}}$

Step 2.3.1.2

Raise $32$ to the power of $2$ .

$\frac{16}{a^{2}} = \frac{1024}{a^{2}}$

Step 3

Solve for $a$ .

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Step 3.1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$16 = 1024$

Step 3.2

Since $16 \neq 1024$ , there are no solutions.

No solution