Simplify (-5x^3)^-2 using only positive exponents

Mathematics

2 answers:

mihalych1998 [28]3 years ago

5 0

Hope you know that x^(-1) = 1/x used this you get

(-5x^3)^-2 = 1/(-5x^3)^2 = 1/{(-5^2)(x^6)} = 1/(25x^6)

hope helped

Alona [7]3 years ago

4 0

$a^{-n}=\dfrac{1}{a^n}\\\\(a^n)^m=a^{n\cdot m}\\\\(a\cdot b)^n=a^n\cdot b^n\\------------------\\\\\left(-5x^3\right)^{-2}=\dfrac{1}{\left(-5x^3\right)^2}=\dfrac{1}{(-5)^2(x^3)^2}=\dfrac{1}{25x^{3\cdot2}}=\boxed{\dfrac{1}{25x^6}}$

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I am so stuck! :( Pls help me!!! I don't get the problem and I don't know how to solve it

Lelu [443]

Answer:

$\frac{n^{2}}{2a}$

Step-by-step explanation:

Just split it up first $\frac{9an^{3}}{18a^{2}n}=\frac{9}{18}\times \frac{a}{a^2} \times\frac{n^3}{n}$
Then 9 divided by 18 can be simplified into the fraction 1/2
What can go into $a$ and $a^2$ ? a itself right, so if you divide a by a you get 1, if you divide $a^2$ by a you get a
Same as the a fraction, if you divide $n^3$ by n you get $n^2$
$\frac{9an^{3}}{18a^{2}n}=\frac{9}{18}\times \frac{a}{a^2} \times\frac{n^3}{n}=\frac{1}{2}\times \frac{1}{a} \times\frac{n^2}{1}=\frac{n^{2}}{2a}$