What number should both sides of the equation be multiplied by to solve for x?x\4.5 = 64564.5

Mathematics

1 answer:

Furkat [3]8 months ago

8 0

Explanation

We are given the equation below:

$\frac{x}{4.5}=6$

We are to determine the value to be multiplied by both sides to solve for x.

This is achieved by multiplying both sides by the LCD (Lowest Common Denominator), in other words, the LCM of the denominators.

In this case, the LCD is 4.5.

Hence, the answer is 4.5

The

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$Use:\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\sqrt[n]{a}=a^\frac{1}{n}\\------------------------\\\\\left(16n^4\right)^{\frac{5}{4}}=16^\frac{5}{4}\left(n^4\right)^\frac{5}{4}=16^{1\frac{1}{4}}n^{4\cdot\frac{5}{4}}=16^{1+\frac{1}{4}}n^5=16^1\cdot16^\frac{1}{4}\cdot n^5\\\\=16\cdot\sqrt[4]{16}\cdot n^5=16\cdot2\cdot n^5=\boxed{32n^5}\\\\\sqrt[4]{16}=2\ because\ 2^4=16\\\\\text{Answer}\ \boxed{\left(16n^4\right)^\frac{5}{4}=32n^5}$