Question

help me please

Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.

Answer 1

First clear the bracket of the inner fraction's numerator. This would allow you to reduce the inner fraction to lowest terms.

Given the expression

$(\frac{(2r^2t)^3}{4t^2})^2$

In order to simplify, note that the numerator and denominator of the fraction

$\frac{(2r^2t)^3}{4t^2}$

have common factors. So, we would first remove the bracket in the numerator. This would allow us to reduce the fraction to lowest terms.

To clear the numerator's bracket, note that

$(2r^2t)^3=(2r^2t)\times(2r^2t)\times(2r^2t)\\=(2\times2\times2)\times(r^2\times r^2\times r^2)\times(t\times t\times t)\\=8\times r^6 \times t^3=8r^6 t^3$

that was long. The shorter way was to do the following

$(2r^2t)^3=2^3\times r^{2\times3}\times t^3=8r^6t^3$

so back to the original question, to simplify

$(\frac{(2r^2t)^3}{4t^2})^2$

we would do

$(\frac{(2r^2t)^3}{4t^2})^2=(\frac{2^3r^{2\times3}t^3}{4t^2})^2\\\\=(\frac{8r^6t^3}{4t^2})^2$

Now that we have removed the bracket from the numerator, we can now accomplish the step of reducing the fraction to lowest terms

$(\frac{8r^6t^3}{4t^2})^2=(\frac{8}{4}\times r^6\times \frac{t^3}{t^2})^2\\=(2\times r^6\times t^{3-2})^2\\=(2\times r^6\times t^1)^2\\=(2r^6t)^2$

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