Trigonometry Examples

${(\frac{1}{4})}^{- m} = 64$

Step 1

Apply the product rule to $\frac{1}{4}$ .

$\frac{1^{- m}}{4^{- m}} = 64$

Step 2

One to any power is one.

$\frac{1}{4^{- m}} = 64$

Step 3

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

$4^{m} = 64$

Step 4

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

$4^{m} = 4^{3}$

Step 5

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

$m = 3$