Question: Thinking Inquiry and problem solving [7 marks] 1. Simplify the following. Your final answer must…

Thinking Inquiry and problem solving [7 marks]

1. Simplify the following. Your final answer must contain only positive exponents. (2a^3b^3)^3 (ab^-2) Simply stating the final expression will result in a mark of zero. [3 marks]

Solution

Simplify the expression inside the parentheses. \[ \frac{2a^{\frac{3}{2}}b^3}{ab^{-2}} \] Simplify the fraction by dividing the coefficients and subtracting the exponents. \[ 2a^{\frac{3}{2} - 1}b^{3 - (-2)} = 2a^{\frac{1}{2}}b^{5} \] Apply the exponent of 3 to each factor. \[ \left(2a^{\frac{1}{2}}b^{5}\right)^3 = 2^{3}a^{\frac{3}{2}}b^{15} = 8a^{\frac{3}{2}}b^{15} \] The simplified expression with only positive exponents is: \[ 8a^{\frac{3}{2}}b^{15} \]