Select the answer which is equivalent to the given expression using your calculator. {:[(6a^(-2))/(5b^(-(2)/(3)))],[a=-3" and "b=64]:} -(32)/(15) (32)/(15) (32)/(45) -(32)/(45)

Question

Select the answer which is equivalent to the given expression using your calculator.  {:[(6a^(-2))/(5b^(-(2)/(3)))],[a=-3" and "b=64]:}  -(32)/(15)  (32)/(15)  (32)/(45)  -(32)/(45)

Bytelearn · Accepted Answer

Substitute Values: Substitute the given values of a and b into the expression. We have the expression $\frac{6a^{-2}}{5b^{-\frac{2}{3}}}$ and the values $a = -3$ and $b = 64$. Let's substitute these values into the expression. $\frac{6(-3)^{-2}}{5(64)^{-\frac{2}{3}}}$Simplify Exponents: Simplify the expression by calculating the exponents. We need to calculate $(-3)^{-2}$ and $64^{-\frac{2}{3}}$. $(-3)^{-2} = \frac{1}{(-3)^2} = \frac{1}{9}$ $64^{-\frac{2}{3}} = \frac{1}{64^{\frac{2}{3}}}$ Since $64 = 4^3$, we can write $64^{\frac{2}{3}}$ as $(4^3)^{\frac{2}{3}} = 4^2 = 16$. So, $64^{-\frac{2}{3}} = \frac{1}{16}$. Now, our expression looks like this: $\frac{6 \cdot \frac{1}{9}}{5 \cdot \frac{1}{16}}$Perform Multiplication and Division: Perform the multiplication and division. Now we multiply the numerators and denominators separately. $\frac{6 \cdot \frac{1}{9}}{5 \cdot \frac{1}{16}} = \frac{6}{9} \cdot \frac{16}{5}$ Simplify the fraction $\frac{6}{9}$ to $\frac{2}{3}$ by dividing both numerator and denominator by 3. $\frac{2}{3} \cdot \frac{16}{5}$ Now multiply the numerators together and the denominators together. $\frac{2 \cdot 16}{3 \cdot 5} = \frac{32}{15}$Determine Sign: Determine the sign of the result. Since both a and b are positive after being raised to their respective powers, the result will be positive. Therefore, the answer is $\frac{32}{15}$.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\begin{array}{c} \frac{6 a^{-2}}{5 b^{-\frac{2}{3}}} \\ a=-3 \text { and } b=64 \end{array}$ $\newline$ $-\frac{32}{15}$ $\newline$ $\frac{32}{15}$ $\newline$ $\frac{32}{45}$ $\newline$ $-\frac{32}{45}$

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