Algebra Examples

$5 \cdot 2^{x} = \frac{5}{16}$

Step 1

Divide each term in $5 \cdot 2^{x} = \frac{5}{16}$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 \cdot 2^{x} = \frac{5}{16}$ by $5$ .

$\frac{5 \cdot 2^{x}}{5} = \frac{\frac{5}{16}}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 \cdot 2^{x}}{5} = \frac{\frac{5}{16}}{5}$

Step 1.2.1.2

Divide $2^{x}$ by $1$ .

$2^{x} = \frac{\frac{5}{16}}{5}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply the numerator by the reciprocal of the denominator.

$2^{x} = \frac{5}{16} \cdot \frac{1}{5}$

Step 1.3.2

Cancel the common factor of $5$ .

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Step 1.3.2.1

Cancel the common factor.

$2^{x} = \frac{5}{16} \cdot \frac{1}{5}$

Step 1.3.2.2

Rewrite the expression.

$2^{x} = \frac{1}{16}$

Step 2

Raise $16$ to the power of $1$ .

$2^{x} = \frac{1}{16^{1}}$

Step 3

Move $16^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{x} = 16^{- 1}$

Step 4

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

$2^{x} = 2^{- 4}$

Step 5

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

$x = - 4$