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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #31 : High School Math

Evaluate the following expresssion.

$(4 - 7)^{2}$

Possible Answers:

$\frac{1}{9}$

Correct answer:

Explanation:

Recall the order of operations (PEMDAS). We want to combine the terms inside our parentheses first. Thus, 4 - 7 = -3 so we have our expression equivalent to:

$(-3)^{2} = 9$ . Don't forget to keep the in parentheses after you get it as the sum.

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Example Question #11 : Operations

$3-7\ast8+4\div2=?$

Possible Answers:

Correct answer:

Explanation:

Remember the order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally" stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction".

$3-7\ast8+4\div2=?$

$3-\left (7\ast8 \right )\left +(4\div2 \right )=$

3-56+2=

-53+2=-51

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Example Question #11 : Operations And Properties

Simplify:

$6-(2+5^{2})$

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations.

First take care of any exponents:

$6-(2+5^{2})$

= 6 - (2 + 25)

Then perform the operations in parentheses:

= 6 - 27

= -21

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Example Question #12 : How To Use The Order Of Operations In Pre Algebra

12+4^2=

Possible Answers:

256

Correct answer:

Explanation:

In terms of order of operations, you must first perform the exponent portions and then add to the 12:

4^2=16

16+12=28

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Example Question #33 : Whole Numbers

Simplify $\frac{8-(3*4)^-^1}{4-3^-^2^}$

Possible Answers:

$\frac{5}{12}$

$\frac{57}{28}$

$\frac{95}{12}$

$\frac{281}{14}$

Correct answer:

$\frac{57}{28}$

Explanation:

Applying the Order of Operations to the numerator, we get:

8-(3*4)^-^1

8 - 12^-^1

$8-\frac{1}{12}$

$\frac{96}{12} - \frac{1}{12}$

$\frac{95}{12}$

Applying the Order of Operations to the denominator, we get:

4-3^-^2

$4-\frac{1}{9}$

$\frac{36}{9} - \frac{1}{9}$

$\frac{35}{9}$

We divide these fractions to get:

$\frac{95}{12} \cdot \frac{9}{35}=\frac{19}{4}\cdot \frac{3}{7}=\frac{57}{28}$

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Example Question #1 : How To Do Exponents In Pre Algebra

$Y^{3}\ast Y^{2}=?$

Possible Answers:

$Y^{6}$

$Y^{4}$

$Y^{5}$

$Y^{2}$

Correct answer:

$Y^{5}$

Explanation:

When you multiply exponents you can simply add the exponents:

$Y^{3}\ast Y^{2}=Y^{\left ( 3+2\right )}=Y^{5}$

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Example Question #2 : How To Do Exponents In Pre Algebra

Evaluate the exponential expression.

$\small (2^3)^2$

Possible Answers:

128

Correct answer:

Explanation:

We can solve this problem in two different ways.

The first way is to evaluate the internal term, $\small 2^3$ , and then square it.

$\small (2^3)^2=(2*2*2)^2=(8)^2$

$\small 8^2=64$

The second method is to use the power rule of exponents, where we multiply the exponents and solve the resulting term.

$(x^a)^b=x^{a*b}$

$\small (2^3)^2=2^{3*2}=2^6=64$

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Example Question #3 : How To Do Exponents In Pre Algebra

Evaluate $\dpi{100} \dpi{100} 9^{-\frac{1}{2}}$ .

Possible Answers:

$-\frac{1}{3}$

$\sqrt{-3}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

The negative sign in the exponent indicates that in order to solve you should use the reciprocal of the integer.

$\dpi{100} 9^{-\frac{1}{2}}=\frac{1}{9^{\frac{1}{2}}}$

$\frac{1}{9^{\frac{1}{2}}}=\frac{1}{\sqrt{9}}$

$\rightarrow\frac{1}{3}$

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Example Question #4 : How To Do Exponents In Pre Algebra

Evaluate $\dpi{100} (5^\frac{1}{2})^{2}$

Possible Answers:

$5^{2}$

$\sqrt{5}$

$\frac{1}{\sqrt{5}}$

$5^{4}$

Correct answer:

Explanation:

The laws of exponents state that when a number is raised to a certain power and then raised to another power then the exponents are multiplied by one another.

$(5^\frac{1}{2})^{2}=5^{(\frac{1}{2}*2)}$

Solve for the exponents.

$(\frac{1}{2}*2)=\frac{1}{2}*\frac{2}{1}$

$\rightarrow \frac{2}{2}\rightarrow1$

Therefore,

$\dpi{100} \dpi{100} (5^\frac{1}{2})^{2}=5^{1}$

$\rightarrow 5$

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Example Question #5 : How To Do Exponents In Pre Algebra

What is $2^{5}=?$

Possible Answers:

Correct answer:

Explanation:

When a number is raised to a power it means that the number is multiplied by itself the same number of times as the number of the power.

In this case is raised to the 5th power so it is equivalent to 2*2*2*2*2

We then perform the necessary multiplication to arrive at the answer of .

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #31 : High School Math

Example Question #11 : Operations

Example Question #11 : Operations And Properties

Example Question #12 : How To Use The Order Of Operations In Pre Algebra

Example Question #33 : Whole Numbers

Example Question #1 : How To Do Exponents In Pre Algebra

Example Question #2 : How To Do Exponents In Pre Algebra

Example Question #3 : How To Do Exponents In Pre Algebra

Example Question #4 : How To Do Exponents In Pre Algebra

Example Question #5 : How To Do Exponents In Pre Algebra

All High School Math Resources

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