QuestionCalculate $2^{-2} \cdot(12 \cdot 3)-5^{3}$ .

Studdy Solution

STEP 1

Assumptions1. The problem is $^{-} \cdot(12 \cdot3)-5^{3}$ . The order of operations 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 need to solve the operation inside the parentheses.
$12 \cdot$

STEP 3

Calculate the result of the operation inside the parentheses.
$12 \cdot3 =36$

STEP 4

Now, substitute the result back into the equation.
$2^{-2} \cdot36 -^{3}$

STEP 5

Next, we need to solve the exponent $2^{-2}$ .Remember that any number raised to the power of -n is equal to1 divided by the number raised to the power of n.
$2^{-2} = \frac{1}{2^{2}}$

STEP 6

Calculate the result of the exponent.
$\frac{1}{2^{2}} = \frac{1}{4} =0.25$

STEP 7

Now, substitute the result back into the equation.
$0.25 \cdot36 -5^{3}$

STEP 8

Next, we need to solve the multiplication $0.25 \cdot36$ .
$0.25 \cdot36$

STEP 9

Calculate the result of the multiplication.
$.25 \cdot36 =9$

STEP 10

Now, substitute the result back into the equation.
$9 -5^{3}$

STEP 11

Next, we need to solve the exponent $5^{3}$ .
$5^{3}$

STEP 12

Calculate the result of the exponent.
$5^{} =125$

STEP 13

Now, substitute the result back into the equation.
$9 -125$

STEP 14

Finally, we need to solve the subtraction $9 -125$ .
$9 -125$

STEP 15

Calculate the result of the subtraction.
$9 -125 = -116$ The solution to the problem $2^{-2} \cdot(12 \cdot3)-5^{3}$ is -116.

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