Question

Pls answer fast first to answer correct is the gets brainliest

Answer 1

Answer:

The answer is the first option; 6^1/12

Step-by-step explanation:

We can simplify the question by using the radical rule to rewrite it as
6^1/3 ÷ 6^1/4

Then we use exponent rule which states that when we are dividing exponents of the same base, we have to subtract them. We see that the exponents are 1/3 and 1/4. So we use basic fractional division, here's the subtraction:

= 1/3 - 1/4
= 4/3 - 3/4 (we criss-crossed)
= 1/12 (we subtracted the denominators and multiplied the denominators)

Now that we have subtracted the exponents, we can write the answer as 6^1/12

Answer 2

Answer:

Option #1: $6\frac{1}{2}$

Step-by-step explanation:

#1: Multiply $\frac{\sqrt[3]{6}}{\sqrt[4]{6}}$ and $\frac{\sqrt[3]{6}}{\sqrt[4]{6}}$:

$\frac{\sqrt[3]{6}}{\sqrt[4]{6}} * \frac{\sqrt[3]{6}}{\sqrt[4]{6}}$

#2: Combine and simplify the denominator:

- Multiply $\frac{\sqrt[3]{6}}{\sqrt[4]{6}}$ by $\frac{\sqrt[3]{6}}{\sqrt[4]{6}}$ = $\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6} \sqrt[4]{6}^3}$

- Raise $\sqrt[4]{6}$ to the power of 1

- Use the power rule $a^{m} a^{n} =a^{m+n}$ to combine exponents: $\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6}^{1+3}}$

- Add 1 and 3

- Rewrite $\sqrt[4]{6}^4$ as 6: $\frac{\sqrt[3]{6} \sqrt[4]{6}^3}{6}$

#3: Simplify the numerator:

- Rewrite the expression using the least common index of 12: $\frac{\sqrt[12]{6^4} \sqrt[12]{216^3}}{6}$

- Combine using the product rule for radicals: $\frac{\sqrt[3]{6^4 *216^3}}{6}$

- Rewrite 216 as $6^3$: $\frac{\sqrt[3]{6^{4}*(6^{3})^{3}}}{6}$

- Multiply the exponents in $(6^{3})^3$: $\frac{\sqrt[12]{6^{4}*6^{9}}}{6}$

- Use the power rule $a^{m}a^{n}=a^{m+n}$ to combine exponents and add $4+9$:

$\frac{\sqrt[12]{6^{13}}}{6}$

- Raise 6 to the power of 16: $\frac{\sqrt[12]{13060694016}}{6}$

- Rewrite 13060694016 as $6^{12}*6$: $\frac{\sqrt[12]{6^{12}*6}}{6}$

- Pull terms out from under the radical: $\frac{6\sqrt[12]{6}}{6}$

#4: Cancel the common factor of 6:

$\frac{\sqrt[12]{6}}{6}=6\frac{1}{2}$

The correct simplified answer for $\frac{\sqrt[3]{6}}{\sqrt[4]{6}}$ is Option #1: $6\frac{1}{2}$.