As we know already, to evaluate numerical expressions with a mix of different operations, we follow the order of operations (PEMDAS).

The same rules apply to numerical expressions with zero and negative exponents. To demonstrate, let's compute the value of (-3)^0 +2^2 \div 2.

To evaluate the given expression, we use PEMDAS.

Notice that \left(-3\right)^{0}=1. So, we obtain

\begin{align*} {\color{blue}\left(-3\right)^{0}} +2^2 \div 2 &=\\[5pt] {\color{blue}1} +2^2 \div 2 &=\\[5pt] 1 +4 \div 2 &=\\[5pt] 1 + 2 &=\\[5pt] 3 &. \end{align*}

FLAG

Calculate 10\div 5^0 + (3^2-5).

EXPLANATION

To evaluate the given expression, we use PEMDAS.

First, we compute the expression inside the parentheses:

\begin{align*} 10\div 5^0 + ({\color{red}9} - {\color{red}5}) = 10\div 5^0 + {\color{red}4} \end{align*}

Next, notice that 5^0=1. So, we obtain:

\begin{align*} 10\div {\color{blue}5^0} + 4 &=\\[3pt] 10\div {\color{blue}1} +4 &=\\[3pt] 10 + 4 &=\\[3pt] 14 \end{align*}

FLAG

$8^2 \div 16 + 11^0=$

a
$15$
b
$8$
c
$4$
d
$17$
e
$5$

$-(3)^2+(-5) \times 2^0=$

a
$-4$
b
$4$
c
$1$
d
$-14$
e
$-1$

$\left(-\dfrac{4}{3}\right)^{\!0} \div (1+3^2) - 3.5 = $

a
$-3.2$
b
$-2.7$
c
$2.9$
d
$3.5$
e
$-3.4$

What is the value of \dfrac{4}{3} \times (-5+3)^{-2} + \dfrac{2}{3} ?

EXPLANATION

To evaluate the given expression, we use PEMDAS.

First, we compute the expression inside the parentheses:

\dfrac{4}{3} \times ({\color{red}-5} + {\color{red}3})^{-2} + \dfrac{2}{3} = \dfrac{4}{3} \times ({\color{red}-2})^{-2} + \dfrac{2}{3}

Next, notice that (-2)^{-2}=\dfrac{1}{(-2)^2} = \dfrac{1}{4}. So, we obtain:

\begin{align*} \require{cancel} \dfrac{4}{3} \times {\color{blue}(-2)^{-2}} + \dfrac{2}{3} &=\\[5pt] \dfrac{4}{3} \times {\color{blue}\dfrac{1}{4}} + \dfrac{2}{3} &=\\[5pt] \dfrac{4\times 1}{3\times 4} + \dfrac{2}{3} &=\\[5pt] \dfrac{\cancel{4}\times 1}{3\times \cancel{4}} + \dfrac{2}{3} &=\\[5pt] \dfrac{1}{3} + \dfrac{2}{3} &=\\[5pt] 1 \end{align*}

FLAG

$5^{-2} \div \dfrac{1}{5}=$

a
$\dfrac{1}{25}$
b
$-25$
c
$5$
d
$\dfrac{1}{5}$
e
$-\dfrac{1}{5}$

$2^{-2} \div \left(\dfrac{1}{4}-1\right)=$

a
$\dfrac{1}{3}$
b
$-6$
c
$\dfrac{1}{6}$
d
$-\dfrac{1}{3}$
e
$3$

Calculate $\dfrac{5}{8} \times 3 - (8-10)^{-3}.$

a
$\dfrac{1}{2}$
b
$-\dfrac{1}{2}$
c
$-2$
d
$2$
e
$-8$

Find the value of 2 + \left(-4\right)^{-2} \div \left( 1.5 + \dfrac{2}{15} \right)^0.

EXPLANATION

To evaluate the given expression, we use PEMDAS.

Any number raised to the power of 0 equals 1. So, we have

\left( 1.5 + \dfrac{2}{15} \right) ^0 = 1.

Next, we evaluate the negative exponent and get

\left(-4\right)^{-2} = \dfrac{1}{(-4)^2} = \dfrac{1}{16}.

Substituting all these values into the expression, we obtain:

\begin{align*} 2 + {\color{blue}\left(-4\right)^{-2}} \div {\color{red}\left( 1.5 + \dfrac{2}{15} \right)^0} &=\\[5pt] 2 + {\color{blue}\dfrac{1}{16}} \div {\color{red}1} &=\\[5pt] 2 + \dfrac{1}{16} &=\\[5pt] \dfrac{32}{16} + \dfrac{1}{16} &=\\[5pt] \dfrac{33}{16} \end{align*}

FLAG

Calculate $\left(\dfrac{5}{8}\right)^0 \times (3.5-1.5)^{-3}.$

a
$2$
b
$\dfrac{1}{8}$
c
$\dfrac{1}{2}$
d
$-\dfrac{1}{4}$
e
$-8$

$18 \div \left(\dfrac{1}{3}\right)^{-2} + \left( \dfrac{1}{101}-0.01 \right) ^0 =$

a
$\dfrac{3}{2}$
b
$1$
c
$2$
d
$\dfrac{4}{3}$
e
$3$

Calculate $\left( \dfrac{8}{7} - \dfrac{1}{16} \right) ^0 -11 \times \left(\dfrac{1}{2}\right)^{-3}.$

a
$89$
b
$-87$
c
$87$
d
$-121$
e
$-89$
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