QuestionSolve $-\frac{1}{6}\left[3-15\left(\frac{1}{3}\right)^{2}\right]$ and choose the correct answer.

Studdy Solution

STEP 1

Assumptions1. We need to solve the expression $-\frac{1}{6}\left[3-15\left(\frac{1}{3}\right)^{}\right]$ . We will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we will solve the operation inside the parentheses, which is $\left(\frac{1}{}\right)^{2}$ .

STEP 3

Calculate the value of $\left(\frac{1}{3}\right)^{2}$ .
$\left(\frac{1}{3}\right)^{2} = \frac{1}{9}$

STEP 4

Substitute the value of $\left(\frac{1}{3}\right)^{2}$ back into the expression.
$-\frac{1}{6}\left[3-15\left(\frac{1}{9}\right)\right]$

STEP 5

Next, perform the multiplication operation inside the brackets, which is $15\left(\frac{1}{9}\right)$ .

STEP 6

Calculate the value of $15\left(\frac{1}{9}\right)$ .
$15\left(\frac{1}{9}\right) = \frac{5}{3}$

STEP 7

Substitute the value of $15\left(\frac{1}{9}\right)$ back into the expression.
$-\frac{1}{6}\left[3-\frac{5}{3}\right]$

STEP 8

Next, perform the subtraction operation inside the brackets, which is $3-\frac{5}{3}$ .

STEP 9

Calculate the value of $3-\frac{5}{3}$ .
$3-\frac{5}{3} = \frac{4}{3}$

STEP 10

Substitute the value of $3-\frac{5}{3}$ back into the expression.
$-\frac{}{6}\left[\frac{4}{3}\right]$

STEP 11

Finally, perform the multiplication operation, which is $-\frac{}{6}\left[\frac{4}{3}\right]$ .

STEP 12

Calculate the value of $-\frac{}{6}\left[\frac{4}{}\right]$ .
$-\frac{}{6}\left[\frac{4}{}\right] = -\frac{2}{9}$ So, the solution to the expression $-\frac{}{6}\left[-15\left(\frac{}{}\right)^{2}\right]$ is $-\frac{2}{9}$ .

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