Pre-Algebra Examples

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

Step 1

Rewrite the equation as $2^{y} = {(\frac{1}{2})}^{3}$ .

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

Step 2

Apply the product rule to $\frac{1}{2}$ .

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

Step 3

One to any power is one.

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

Step 4

Move $2^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 5

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

$y = - 3$