Basic Math Examples

$\sqrt{2^{y}} = \frac{1}{4}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2^{y}}$ as $2^{\frac{y}{2}}$ .

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

Step 2

Raise $4$ to the power of $1$ .

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

Step 3

Move $4^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{\frac{y}{2}} = 4^{- 1}$

Step 4

Create equivalent expressions in the equation that all have equal bases.

$2^{\frac{y}{2}} = 2^{- 2}$

Step 5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$\frac{y}{2} = - 2$

Step 6

Solve for $y$ .

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Step 6.1

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 \cdot - 2$

Step 6.2

Simplify both sides of the equation.

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Step 6.2.1

Simplify the left side.

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 \cdot - 2$

Step 6.2.1.1.2

Rewrite the expression.

$y = 2 \cdot - 2$

Step 6.2.2

Simplify the right side.

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Step 6.2.2.1

Multiply $2$ by $- 2$ .

$y = - 4$