Precalculus Examples

${(\frac{81^{\frac{1}{2}}}{3^{- 1}})}^{0}$

Step 1

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

${(81^{\frac{1}{2}} \cdot 3)}^{0}$

Step 2

Rewrite $81$ as $3^{4}$ .

${({(3^{4})}^{\frac{1}{2}} \cdot 3)}^{0}$

Step 3

Multiply the exponents in ${(3^{4})}^{\frac{1}{2}}$ .

Tap for more steps...

Step 3.1

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

${(3^{4 (\frac{1}{2})} \cdot 3)}^{0}$

Step 3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1

Factor $2$ out of $4$ .

${(3^{2 (2) \frac{1}{2}} \cdot 3)}^{0}$

Step 3.2.2

Cancel the common factor.

${(3^{2 \cdot 2 \frac{1}{2}} \cdot 3)}^{0}$

Step 3.2.3

Rewrite the expression.

${(3^{2} \cdot 3)}^{0}$

Step 4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(3^{2 + 1})}^{0}$

Step 5

Add $2$ and $1$ .

${(3^{3})}^{0}$

Step 6

Multiply the exponents in ${(3^{3})}^{0}$ .

Tap for more steps...

Step 6.1

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

$3^{3 \cdot 0}$

Step 6.2

Multiply $3$ by $0$ .

$3^{0}$

Step 7

Anything raised to $0$ is $1$ .

$1$