use the properties of exponents to simplify the expression. write with positive exponents. assume that all…

use the properties of exponents to simplify the expression. write with positive exponents. assume that all variables represent positive real numbers.\n\\( \\frac { b ^ { \\frac { 2 } { 3 } } b ^ { \\frac { 2 } { 3 } } } { - b ^ { \\frac { 1 } { 3 } } } \\)\n\\( \\frac { b ^ { \\frac { 2 } { 3 } } b ^ { \\frac { 2 } { 3 } } } { - b ^ { \\frac { 1 } { 3 } } } = \\)

use the properties of exponents to simplify the expression. write with positive exponents. assume that all variables represent positive real numbers.\n\\( \\frac { b ^ { \\frac { 2 } { 3 } } b ^ { \\frac { 2 } { 3 } } } { - b ^ { \\frac { 1 } { 3 } } } \\)\n\\( \\frac { b ^ { \\frac { 2 } { 3 } } b ^ { \\frac { 2 } { 3 } } } { - b ^ { \\frac { 1 } { 3 } } } = \\)

Answer

Explanation:

Step1: Use the product rule of exponents (a^m\times a^n=a^{m + n})

For the numerator (b^{\frac{2}{3}}b^{\frac{2}{3}}), we have (b^{\frac{2}{3}+\frac{2}{3}}=b^{\frac{4}{3}}). So the expression becomes (\frac{b^{\frac{4}{3}}}{-b^{\frac{1}{3}}}).

Step2: Use the quotient rule of exponents (\frac{a^m}{a^n}=a^{m - n})

Here (a = b), (m=\frac{4}{3}), (n=\frac{1}{3}). Then (b^{\frac{4}{3}-\frac{1}{3}}=b^{\frac{4 - 1}{3}}=b^{1}). So (\frac{b^{\frac{4}{3}}}{-b^{\frac{1}{3}}}=-b^{1}).

Answer:

(-b)