Question

Simplify open parentheses x to the 4 fifths power close parentheses to the 3 sevenths power.

x to the 7 twelfths power
x to the 12 over 35 power
x to the 13 over 35 power
x to the 43 over 35 power

Answer 1

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Answer 2

`x^(12)/(35)`

Explanation:

Here let us first write our expression

It says, x raise to 4 5th power i.e 4 by 5 , again raise to 3 7th power i.e 3 by 7

or
`(x^{(4)/(5)})^(3)/(7)`

Now in this we apply the rule of product of exponents . The rule is like this.

`(x^(m))^(n)=x^(mn)`

Let us apply the rule in our problem

`(x^{(4)/(5)})^(3)/(7) = x^{(4)/(5)*(3)/(7)}`

`x^{(4)/(5)*(3)/(7)} = x^{(4*3)/(5*7)}`

`x^{(4*3)/(5*7)}=x^{(12)/(35)}`

Which is x to the 12 over 35 hence our b option is correct