QuestionSimplify $\left(\frac{3 a}{b^{-3}}\right)^{3}$ using only positive exponents.

Studdy Solution

STEP 1

Assumptions1. The expression to be simplified is $\left(\frac{3 a}{b^{-3}}\right)^{3}$ . . The exponent rule states that $(a^m)^n = a^{mn}$ .
3. The exponent rule also states that $a^{-n} = \frac{1}{a^n}$ .

STEP 2

First, we will apply the exponent rule to the expression. This rule states that $(a^m)^n = a^{mn}$ .
\left(\frac{ a}{b^{-}}\right)^{} = \left(^ a^\right) / \left(b^{-*}\right)

STEP 3

Now, calculate the values of $3^3$ and $-3*3$ .
$\left(\frac{3 a}{b^{-3}}\right)^{3} = \left(27 a^3\right) / \left(b^{-9}\right)$

STEP 4

Next, we will apply the exponent rule that states $a^{-n} = \frac{1}{a^n}$ to $b^{-9}$ .
$\left(\frac{3 a}{b^{-3}}\right)^{3} = \left(27 a^3\right) / \left(\frac{1}{b^9}\right)$

STEP 5

Now, simplify the expression by multiplying the numerator and denominator by $b^9$ .
$\left(\frac{3 a}{b^{-3}}\right)^{3} =27 a^3 b^9$ The simplified expression with only positive exponents is $27 a^3 b^9$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms