Rewrite the expression in the form a^n a^5xa^-3

Mathematics

1 answer:

erik [133]3 years ago

6 0

<h3>Answer: a^2</h3>

Work Shown:

I'm assuming the "x" means "multiply", and it is not a variable.

a^5 * a^(-3) = a^(5+(-3)) = a^(5-3) = a^2

The rule I'm using is

a^b*a^c = a^(b+c)

The base is always the same. We add the exponents.

The expression a^2 is in the form a^n with n = 2.

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Scilla [17]

Answer:

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Step-by-step explanation:

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5 0

3 years ago

The square of a number decreased by 3 times the number 28 find all possible values for the number

stealth61 [152]

Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number

Answer:

The possible values of number are 7 and -4

Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

$a^2 - 3a = 28$

$a^2 - 3a - 28 = 0$

Let us solve the above quadratic equation

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

$\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28$

$\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}$