Trigonometry Examples

$2^{y - 3} = \frac{1}{16}$

Step 1

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

$2^{y - 3} = \frac{1}{16^{1}}$

Step 2

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

$2^{y - 3} = 16^{- 1}$

Step 3

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

$2^{y - 3} = 2^{- 4}$

Step 4

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

$y - 3 = - 4$

Step 5

Move all terms not containing $y$ to the right side of the equation.

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Step 5.1

Add $3$ to both sides of the equation.

$y = - 4 + 3$

Step 5.2

Add $- 4$ and $3$ .

$y = - 1$