Answered: "Express the following fraction in simplest form using..."

High School

Destini Jones

Answered question

2022-08-31

Express the following fraction in simplest form using only positive exponents.

$\frac{15 h}{3 (h^3)^2}$

Answer & Explanation

Mr Solver

Skilled2023-05-25Added 147 answers

The given fraction is:

\frac{15 h}{3 (h^{3})^{2}}

First, let's simplify the numerator:

15 h

is already in its simplest form.
Now, let's simplify the denominator:

(h^{3})^{2} = h^{3 \cdot 2} = h^{6}

Now, we can rewrite the fraction in simplest form:

\frac{15 h}{3 (h^{3})^{2}} = \frac{15 h}{3 h^{6}}

Next, we can simplify the fraction by canceling out common factors between the numerator and denominator. In this case, we can divide both the numerator and denominator by 3:

\frac{15 h}{3 h^{6}} = \frac{5 h}{h^{6}}

Finally, to express the fraction with positive exponents only, we can rewrite

h^{6}

\frac{1}{h^{- 6}}

\frac{5 h}{h^{6}} = \frac{5 h}{\frac{1}{h^{- 6}}} = 5 h \cdot h^{- 6} = 5 h^{1 + (- 6)} = 5 h^{- 5}

Therefore, the fraction

\frac{15 h}{3 (h^{3})^{2}}

can be expressed in simplest form as

5 h^{- 5}

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