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

${(x^{\frac{2}{9}})^{\frac{3}{8}} * x^\frac{5}{17} * x^\frac{1}{12} * x^\frac{11}{72} * x^\frac{43}{72}$

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

=${(x^{\frac{1}{12}}) }* x^\frac{5}{17} * x^\frac{1}{12} * x^\frac{11}{72} * x^\frac{43}{72}$

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)

=${x^{\frac{1}{12}+\frac{5}{17} +\frac{1}{12} +\frac{11}{72} +\frac{43}{72} }$

=$x^\frac{247}{204}$

Answer 2

Answer:

Power x to the 1 twelfth  

Step-by-step explanation:

The given expression is:

$({x^{\frac{2}{9}}})^{\frac{3}{8}}$

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

$({x^{\frac{2}{9}}})^{\frac{3}{8}} = x^{(\frac{2}{9} \times \frac{3}{8})} = x^{\frac{1}{12}}$