Question

6a to the 3/4 power a=16

Answer 1

Answer:

The answer is 48

Step-by-step explanation:

* Lets explain how to solve the problem

- The radical can be written as a fraction power:

 $\sqrt[n]{x^{m} }=x^{\frac{m}{n}}$

- We can simplify the fraction power by factorize the base of the power

 to numbers divisible by the power if it could

- Ex: $25^{\frac{1}{2}}$ we can factorize 25 to 5² and then

 make $[(5)^{2}]^{\frac{1}{2}}=(5)^{2*\frac{1}{2}}=5$

* Lets solve the problem

- We want to find the value of $6a^{\frac{3}{4}}$ , where a = 16

- Substitute the value of a by 16

∴ $6(16)^{\frac{3}{4}}$

- Lets factorize 16

∵ 16 can be written as 2 × 2 × 2 × 2

∴ $16=2^{4}$

- Replace 16 by $2^{4}$

∴ $6(2^{4})^{\frac{3}{4}}=6(2^{4*\frac{3}{4}})=6(2^{3})$

- Now solve 2³

∵ 2³ = 8

∴ 6(8) = 48

∴ $6a^{\frac{3}{4}}$ = 48

* The answer is 48