Question

Simplify open parentheses x to the 2 ninths power close parentheses to the 3 eighths power. x to the 5 seventeenths power x to the 1 twelfth power x to the 11 over 72 power x to the 43 over 72 power

Answer 1

Power x to the 1 twelfth

Explanation:

The given expression is:

`({x^{(2)/(9)}})^{(3)/(8)}`

In order to simplify an exponential expression which is inside another exponential expression, we have to multiply the exponents. In this case the exponents are 2/9 and 3/8, so

`({x^{(2)/(9)}})^{(3)/(8)} = x^{((2)/(9) * (3)/(8))} = x^{(1)/(12)}`

Answer 2

`{(x^{(2)/(9)})^{(3)/(8)} * x^(5)/(17) * x^(1)/(12) * x^(11)/(72) * x^(43)/(72)`

2/9 times 3/8 = 1/12 , So

=
`{(x^{(1)/(12)}) }* x^(5)/(17) * x^(1)/(12) * x^(11)/(72) * x^(43)/(72)`

Now we add all the exponents , as by the rule of exponents if the base is same and the terms are in multiplication , then we add the exponents , i.e. a^m * a^n = a^(m+n)

=
`{x^{(1)/(12)+(5)/(17) +(1)/(12) +(11)/(72) +(43)/(72) }`

=
`x^(247)/(204)`