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High School Math : Pre-Algebra

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Example Questions

Example Question #6 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify (x^3)(x^8)

Possible Answers:

$x^{24}$

$x^{11}$

$x^{13}$

$x^{14}$

Correct answer:

$x^{11}$

Explanation:

When multiplying the same variable raised to different powers, add the powers of each term together. In this case, add and together to find the power of the answer, .

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Example Question #7 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the exponential expression.

$\small [(3x^2y^2)(4xy^3)]^0$

Possible Answers:

$\small 12x^3y^5$

undefined

Correct answer:

Explanation:

$\small [(3x^2y^2)(4xy^3)]^0$

Any number to the "zero" power is equal to .

(anything)^0=1

$\small [(3x^2y^2)(4xy^3)]^0=[12x^3y^5]^0=1$

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Example Question #561 : Pre Algebra

Evaluate:

$x^{(2x-2)}*x^{(4-2x)}$

Possible Answers:

$x^{4x-6}$

$x^{2}$

$x^{4-x}$

$x^{2x-4}$

$x^{2x}$

Correct answer:

$x^{2}$

Explanation:

The product rule for exponents states that when like numbers are raised to a certain power, their exponents are added to one another.

$x^{m}*x^{n}=x^{(m+n)}$

$x^{2x-2}*x^{4-2x}=x^{(2x-2)+(4-2x)}$

Solve for the exponent equation.

(2x-2)+(4-2x)=2x-2+4+-2x

$\rightarrow 2$

Therefore,

$\dpi{100} x^{2x-2}*x^{4-2x}=x^{2}$ .

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Example Question #1021 : High School Math

If A = 3x^2 + 26 x +108

and

B= 12x-13 ,

what is A-B ?

Possible Answers:

14x+95

$3x^{2}+14x+121$

3x^2+48x+131

14x+131

3x^2+14x+95

Correct answer:

$3x^{2}+14x+121$

Explanation:

To solve we must first write out what A-B is:

A-B=(3x^2+26x+108)-(12x-13)

Now,we can simplify. However, notice that when subtracting these terms, we subtract all terms in the parentheses. Remember when we subtract a negative number, it is the same as adding the number. This is illustrated in the simplification below.

(3x^2+26x+108)-(12x-13) = 3x^2+26x+108 - 12x- (-13)

This simplifies to 3x^2+26x+108 - 12x +13

Now we can combine like terms. Let's put those together and then simplify

3x^2+26x+108 - 12x +13=3x^2+(26x - 12x)+(108 +13) = 3x^2+14x+121

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Example Question #1022 : High School Math

Simplify the expression below.

3x + 4 - (2x + 6)

Possible Answers:

5x - 2

x + 2

x + 10

x - 2

5x + 10

Correct answer:

x - 2

Explanation:

3x + 4 - (2x + 6)

When simplifying the addition or subtraction of polynomials, we want to combine like terms. First, when we have a negative sign outside our parentheses, we know that we need to distribute that negative; think of it as an imaginary and use the distributive property).

3x + 4 - (2x + 6) = 3x + 4 - 2x - 6

Then, we combine our like terms. Be careful when subtracting.

Rearrange the expression.

3x + 4 - 2x - 6 = 3x - 2x + 4 - 6

Combine terms and simplify.

3x-2x+4-6 = x + (-2) = x - 2

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Example Question #1023 : High School Math

Simplify the expression.

$\small x^2+4x^2-3x+2x-7-3x^2$

Possible Answers:

$\small 7x^2-5x-7$

$\small -2x^2-x-7$

$\small 2x^2-x-7$

$\small 8x^2-x-7$

Correct answer:

$\small 2x^2-x-7$

Explanation:

$\small x^2+4x^2-3x+2x-7-3x^2$

Combine like terms.

$\small (x^2+4x^2-3x^2)+(-3x+2x)-7$

$\small x^2+4x^2-3x^2=2x^2$

$\small -3x+2x=-x$

$\small -7=-7$

Add the terms together.

$\small 2x^2+(-x)+(-7)=2x^2-x-7$

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Example Question #1 : How To Add And Subtract Polynomials In Pre Algebra

What is the sum of $10x^{2}+7x+5$ and $\dpi{100} 3x^{2}-9x-8$ ?

Possible Answers:

$\dpi{100} 13x^{2}-16x-13$

$\dpi{100} 3x^{2}+2x+5$

$\dpi{100} 7x^{2}-2x+13$

$\dpi{100} 10x^{2}-x-3$

$13x^{2}-2x-3$

Correct answer:

$13x^{2}-2x-3$

Explanation:

In order to solve the problem, simply add the equations.

$(10x^{2}+7x+5)+(3x^{2}-9x-8)$

$=10x^{2}+7x+5+3x^{2}-9x-8$

Combine like terms.

$=(10x^{2}+3x^{2})+(7x-9x)+(5-8)$

Solve.

$=13x^{2}-2x-3$

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Example Question #2 : How To Add And Subtract Polynomials In Pre Algebra

What is $3x^{5}-5x^{5}$ ?

Possible Answers:

$-2x^{5}$

$2x^{5}$

Correct answer:

$-2x^{5}$

Explanation:

When subtracting polynomials you only subtract the integers in front of like termed variables raised to the same power.

So in this case we take the numbers from in front of the variables and subtract them to get 3-5=-2

After subtraction we add the variable $x^{5}$ to get $-2x^{5}$ .

The answer is $-2x^{5}$ .

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Example Question #31 : Polynomials

Simplify: $\frac{x^6}{x^2}$

Possible Answers:

$x^{4}$

$x^{12}$

$x^{8}$

$x^{3}$

$x^{1}$

Correct answer:

$x^{4}$

Explanation:

According to exponent laws, if the bases are the same for the two numbers being divided, you keep the base and subtract the exponents.

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Example Question #32 : Polynomials

Simplify:

$4\sqrt{5} + 3\sqrt{5}$

Possible Answers:

$7\sqrt{5}$

$7\sqrt{25}$

$12\sqrt{5}$

Correct answer:

$7\sqrt{5}$

Explanation:

Because both terms have the same radical, $\sqrt{5}$ , you can combine terms.

$(4+3) \sqrt{5})$ equals $7\sqrt{5}$

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High School Math : Pre-Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #6 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #7 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #561 : Pre Algebra

Example Question #1021 : High School Math

Example Question #1022 : High School Math

Example Question #1023 : High School Math

Example Question #1 : How To Add And Subtract Polynomials In Pre Algebra

Example Question #2 : How To Add And Subtract Polynomials In Pre Algebra

Example Question #31 : Polynomials

Example Question #32 : Polynomials

All High School Math Resources

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