Algebra Examples

$y = \frac{1}{4} {(4)}^{x}$ for $x = \frac{3}{2}$

Step 1

Replace all occurrences of $x$ with $\frac{3}{2}$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $y = \frac{1}{4} \cdot 4^{x}$ with $\frac{3}{2}$ .

$y = \frac{1}{4} \cdot 4^{\frac{3}{2}}$

$x = \frac{3}{2}$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $\frac{1}{4} \cdot 4^{\frac{3}{2}}$ .

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Step 1.2.1.1

Simplify the expression.

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Step 1.2.1.1.1

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

$y = \frac{1}{4} \cdot {(2^{2})}^{\frac{3}{2}}$

$x = \frac{3}{2}$

Step 1.2.1.1.2

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

$y = \frac{1}{4} \cdot 2^{2 (\frac{3}{2})}$

$x = \frac{3}{2}$

$y = \frac{1}{4} \cdot 2^{2 (\frac{3}{2})}$

$x = \frac{3}{2}$

Step 1.2.1.2

Cancel the common factor of $2$ .

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Step 1.2.1.2.1

Cancel the common factor.

$y = \frac{1}{4} \cdot 2^{2 (\frac{3}{2})}$

$x = \frac{3}{2}$

Step 1.2.1.2.2

Rewrite the expression.

$y = \frac{1}{4} \cdot 2^{3}$

$x = \frac{3}{2}$

$y = \frac{1}{4} \cdot 2^{3}$

$x = \frac{3}{2}$

Step 1.2.1.3

Raise $2$ to the power of $3$ .

$y = \frac{1}{4} \cdot 8$

$x = \frac{3}{2}$

Step 1.2.1.4

Cancel the common factor of $4$ .

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Step 1.2.1.4.1

Factor $4$ out of $8$ .

$y = \frac{1}{4} \cdot (4 (2))$

$x = \frac{3}{2}$

Step 1.2.1.4.2

Cancel the common factor.

$y = \frac{1}{4} \cdot (4 \cdot 2)$

$x = \frac{3}{2}$

Step 1.2.1.4.3

Rewrite the expression.

$y = 2$

$x = \frac{3}{2}$

$y = 2$

$x = \frac{3}{2}$

$y = 2$

$x = \frac{3}{2}$

$y = 2$

$x = \frac{3}{2}$

$y = 2$

$x = \frac{3}{2}$

Step 2

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{3}{2}, 2)$