Simplify the expression $(a^2)^5(2x^2)^4\over2^5(a^3)^3(x^3)^2$

Question

Can anybody please provide a step by step solution to the following expression ?

$$(a^2)^5(2x^2)^4\over2^5(a^3)^3(x^3)^2$$

Answer 1

Hint: $(a^2)^5 = a^{2 \cdot 5} = a^{10}.$

Another hint:

$$\frac{a^8}{a^5} = a^{8-5} = a^3.$$

Your expression is

$$(a^2)^5(2x^2)^4\over2^5(a^3)^3(x^3)^2$$

By applying the first hint, you arrived at this expression in the comments:

$$\frac{a^{10} \cdot 16 x^8}{32 \cdot a^9 x^6}$$

Answer 2

First will show you laws of indices :-

$$a^n * a^m = a^{m+n}$$ $$\frac{a^n}{a^m} = a^{n-m}$$ $$a^n * b^n = (ab)^n$$ $$\frac{a^n}{b^n} = (\frac{a}{b})^n$$ $$(a^n)^m= a^{m*n}$$

Now we will solve your $expression$ with these laws.

$$(a^2)^5(2x^2)^4\over2^5(a^3)^3(x^3)^2$$ $$\frac{(a^{10})(16x^{8})}{32(a^9)(x^6)} \cdots \rightarrow (a^n)^m= a^{m*n}$$ $$\frac{(a^1)(x^{2})}{2} \cdots \rightarrow \frac{a^n}{a^m} = a^{n-m}$$ $$(a)(x^{2})\over2$$

Simple nah.

Answer 3

$$\frac {(a^2)^5(2x^2)^4}{2^5(a^3)^3(x^3)^2} = \frac {a^{10}16x^8}{32a^9x^6} =0.5ax^{2}$$ as for the laws on how to perform this see here: https://en.wikipedia.org/wiki/Exponentiation#Identities_and_properties