Algebra Examples

${(3 t^{\frac{1}{6}})}^{3} {(2 t^{0})}^{- 3}$

Step 1

Apply the product rule to $3 t^{\frac{1}{6}}$ .

$3^{3} {(t^{\frac{1}{6}})}^{3} {(2 t^{0})}^{- 3}$

Step 2

Raise $3$ to the power of $3$ .

$27 {(t^{\frac{1}{6}})}^{3} {(2 t^{0})}^{- 3}$

Step 3

Multiply the exponents in ${(t^{\frac{1}{6}})}^{3}$ .

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Step 3.1

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

$27 t^{\frac{1}{6} \cdot 3} {(2 t^{0})}^{- 3}$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $6$ .

$27 t^{\frac{1}{3 (2)} \cdot 3} {(2 t^{0})}^{- 3}$

Step 3.2.2

Cancel the common factor.

$27 t^{\frac{1}{3 \cdot 2} \cdot 3} {(2 t^{0})}^{- 3}$

Step 3.2.3

Rewrite the expression.

$27 t^{\frac{1}{2}} {(2 t^{0})}^{- 3}$

Step 4

Anything raised to $0$ is $1$ .

$27 t^{\frac{1}{2}} {(2 \cdot 1)}^{- 3}$

Step 5

Multiply $2$ by $1$ .

$27 t^{\frac{1}{2}} \cdot 2^{- 3}$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$27 t^{\frac{1}{2}} \cdot \frac{1}{2^{3}}$

Step 7

Raise $2$ to the power of $3$ .

$27 t^{\frac{1}{2}} \cdot \frac{1}{8}$

Step 8

Multiply $27 t^{\frac{1}{2}} \frac{1}{8}$ .

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Step 8.1

Combine $27$ and $\frac{1}{8}$ .

$t^{\frac{1}{2}} \frac{27}{8}$

Step 8.2

Combine $t^{\frac{1}{2}}$ and $\frac{27}{8}$ .

$\frac{t^{\frac{1}{2}} \cdot 27}{8}$

Step 9

Move $27$ to the left of $t^{\frac{1}{2}}$ .

$\frac{27 t^{\frac{1}{2}}}{8}$