Question

simplify the expression.

\\v^{-3} 8^0 x^9\\

\\\frac{?^{ }}{ ^{ }}\\

Explanation:

Identify the given expression

We are given the algebraic expression:

$$ v^{-3} 8^{0} x^{9} $$

Our goal is to simplify this expression so that it contains only positive exponents.

Apply the zero exponent rule

The zero exponent rule states that any non-zero base raised to the power of \(0\) is equal to \(1\):

$$ a^0 = 1 \quad (a eq 0) $$

Applying this rule to \(8^0\):

$$ 8^0 = 1 $$

Substituting this back into the expression gives:

$$ v^{-3} \cdot 1 \cdot x^{9} = v^{-3} x^{9} $$

Apply the negative exponent rule

The negative exponent rule states that a base raised to a negative power is equal to its reciprocal raised to the positive power:

$$ b^{-n} = \frac{1}{b^n} \quad (b eq 0) $$

Applying this rule to \(v^{-3}\):

$$ v^{-3} = \frac{1}{v^3} $$

Combine the terms into a single fraction

Now, we multiply the simplified parts together:

$$ \frac{1}{v^3} \cdot x^9 = \frac{x^9}{v^3} $$

This expression is fully simplified and contains only positive exponents.

Answer:

Simplify the expression.

\(v^{-3}8^{0}x^{9} =\) <blank>\(\frac{x^9}{v^3}\)</blank>