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hammer [34]
3 years ago
7

What is the monomial if a square of a monomial is: 0.0001*a^8*x^4

Mathematics
1 answer:
Georgia [21]3 years ago
7 0

Answer:

Monomial 0.0001\cdot a^8\cdot x^4 is a square of monomial 0.01\cdot a^4\cdot x^2

Step-by-step explanation:

Given monomial 0.0001\cdot a^8\cdot x^4

Using property (a^m)^n=a^{m\cdot n}, note that

0.0001=(0.01)^2\\ \\a^8=(a^4)^2\\ \\x^4=(x^2)^2

So,

0.0001\cdot a^8\cdot x^4=(0.01)^2\cdot (a^4)^2\cdot (x^2)^2.

Now use property (a\cdot b)^n=a^n\cdot b^n to rewrite the previous expression:

(0.01)^2\cdot (a^4)^2\cdot (x^2)^2=(0.01\cdot a^4\cdot x^2)^2

Hence, monomial 0.0001\cdot a^8\cdot x^4 is a square of monomial 0.01\cdot a^4\cdot x^2

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