3 years ago

Write 625 using exponents in as many ways as you can

1 answer:

5 0

First, you can factor out 625 using the 'tree' method or the 'ladder' method.
625
/ \
5 125
/ \
5 25
/ \
5 5
This means you can say that 625=5 to the power of 4
If your problem requires you to use only whole integers with exponents, then that would be the only way.
If not, then you can also do 625=25*5²

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What is the following product? Assume x>/=0 ^3sqrt(x^2)*^sqrtx^3

RoseWind [281]

Answer:

$x(\sqrt[12]{x^5} )$

Step-by-step explanation:

We need to remember 2 rules when doing these:

1. $\sqrt[n]{x^a} =x^{\frac{a}{n}}$

2. $x^a*x^b=x^{ab}$

Using these 2 rules, we can simplify the product (steps shown below):

$\sqrt[3]{x^2} *\sqrt[4]{x^3} \\=x^{\frac{2}{3}}*x^{\frac{3}{4}}\\=x^{\frac{2}{3}+\frac{3}{4}}\\=x^{\frac{17}{12}}\\=x^{\frac{12}{12}+\frac{5}{12}}\\=x(x^{\frac{5}{12}})\\=x(\sqrt[12]{x^5} )$