QuestionSimplify the expression $5\left(a b^{-1}\right)$ using exponent properties and show only positive exponents.

Studdy Solution

STEP 1

Assumptions1. The expression given is $5\left(a b^{-1}\right)$ . We are to simplify the expression using the properties of exponents3. The final answer should only include positive exponents

STEP 2

We start by applying the property of exponents that states $a^{-n} =1/a^n$ . This property allows us to rewrite $b^{-1}$ as $1/b$ .
$5\left(a b^{-1}\right) =5\left(a \times \frac{1}{b}\right)$

STEP 3

Next, we apply the distributive property of multiplication over addition, which states that $a(b + c) = ab + ac$ . In this case, we are distributing $5$ over the terms inside the parenthesis.
$5\left(a \times \frac{1}{b}\right) =5a \times \frac{5}{b}$

STEP 4

Finally, we simplify the expression by multiplying the numerical coefficients together.
$a \times \frac{}{b} = \frac{25a}{b}$ So, the simplified form of the given expression with only positive exponents is $\frac{25a}{b}$ .

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