Question

simplify the following
$3 {}^{4 } \times 2 {}^{5} \times 9 \\ 2 {}^{5} \times 27$

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Answer 1

Step-by-step explanation:

\(\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{ac}{bd} \qquad \left(b\ne 0; d\ne 0\right)\)

\(\dfrac{a}{b}+\dfrac{c}{b}=\dfrac{a+c}{b} \qquad \left(b\ne 0\right)\)

\(\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times \dfrac{d}{c}=\dfrac{ad}{bc} \qquad \left(b\ne 0; c\ne 0; d\ne 0\right)\)

Note: dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,

\[\frac{x^{2} + 3x}{x + 3}\]

has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.

\begin{align*} \frac{{x}^{2} + 3x}{x + 3} & = \frac{x\left(x + 3\right)}{x + 3}\\ & =x \qquad \qquad \left(x\ne -3\right) \end{align*}

If \(x=-3\) then the denominator, \(x + 3 = 0\) and the fraction is undefined.

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