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Pre-Algebra : Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #132 : Polynomials

Solve: $(x^3)^2 \cdot (x^2)^3$

Possible Answers:

2x^5

$x^{12}$

2x^6

$x^{10}$

$x^{25}$

Correct answer:

$x^{12}$

Explanation:

Simplify the first two terms using the product rule of exponents. When the base of some power is squared, we can simply multiply the two powers together.

$(x^3)^2 \cdot (x^2)^3 = x^{3\times 2} \cdot x^{2\times 3}$

Simplify the powers.

$x^{3\times 2} \cdot x^{2\times 3} =x^6 \cdot x^6$

Use the power rule to add the powers since the bases are alike.

$x^6 \cdot x^6 = x^{6+6} = x^{12}$

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Example Question #37 : Product Rule Of Exponents

Solve

(5x^2)(-3x^4)

Possible Answers:

15x^6

2x^8

-15x^8

-15x^6

2x^6

Correct answer:

-15x^6

Explanation:

If a variable has an exponent with the value of a, it means we are taking that variable and mulitplying it by itself a times. For example,

x^2 = x*x

x^3 = x*x*x

and so on.

So when we multiply

(5x^2)(-3x^4)

we can expand it to look like

(5*x*x)(-3*x*x*x*x)

If we multiply, we get

-15*x*x*x*x*x*x

which equals

-15x^6

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Example Question #541 : Pre Algebra

Simplify the following:

$x^5 \cdot x^2$

Possible Answers:

x^7

x^2

$x^{10}$

x^3

$x^{52}$

Correct answer:

x^7

Explanation:

When you multiply two terms together with the same base, you add the exponents. So,

$x^5 \cdot x^2 = x^{5 + 2} = x^7$

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Example Question #39 : Product Rule Of Exponents

Simplify the following

$x^4 \cdot y^2 \cdot x^{-2} \cdot y$

Possible Answers:

$2x^2 \cdot 2y^3$

$x^2 \cdot y^2$

$x^2 \cdot y^3$

$x^{-8} \cdot y^2$

$x^6 \cdot y^2$

Correct answer:

$x^2 \cdot y^3$

Explanation:

When multiplying terms with the same base, we add the exponents. Therefore,

$x^4 \cdot y^2 \cdot x^{-2} \cdot y$

can be written as

$x^{4+ -2} \cdot y^{2 + 1}$

$x^2 \cdot y^3$

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Example Question #542 : Pre Algebra

Simplify the following expression:

6x^3*8x^7

Possible Answers:

$14x^{10}$

$48x^{21}$

$14x^{21}$

$48x^{10}$

Correct answer:

$48x^{10}$

Explanation:

Simplify the following expression:

6x^3*8x^7

So, we are multiplying exponents. When doing so, we need to treat the numbers out in front like regular multiplication, and add the exponents:

$(6*8)x^{3+7}=48x^{10}$

So we have our answer:

$48x^{10}$

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Example Question #543 : Pre Algebra

Which answer shows the solution to:

(9^3)^2^1

Possible Answers:

9^1^8

9^7

9^2^4

9^1^0

9^6^3

Correct answer:

9^6^3

Explanation:

A question in product format like this you must multiply the exponents.

9^3^*^2^1

= 9 ^6^3

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Example Question #42 : Product Rule Of Exponents

Simplify the following:

$x^{-3} \cdot x^5$

Possible Answers:

2x^2

x^2

$2x^{-15}$

$x^{-15}$

$x^{-8}$

Correct answer:

x^2

Explanation:

The product rule for exponents states then when you have the same base multiplied together, you add the exponents. So,

$x^{-3} \cdot x^5$

can be written as

$x^{-3 + 5}$

x^2

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Example Question #544 : Pre Algebra

Simplify the following:

$x^{10}*x^2$

Possible Answers:

None of the above

$x^{12}$

$x^{20}$

x^5

x^8

Correct answer:

$x^{12}$

Explanation:

When you multiply exponents you will end up adding the two numbers so you will get:

$x^{10+2}$ which is $x^{12}$

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Example Question #545 : Pre Algebra

Evaluate the expression if x=3 .

3x^2-4x+12

Possible Answers:

Correct answer:

Explanation:

We can replace each instance of in the original expression with 3.

$3x^2-4x+12\rightarrow 3(3)^2-4(3)+12$

Now, solve using order of operations:

3(9)-4(3)+12

27-12+12

15+12

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Example Question #2 : Solving Polynomials

Evaluate the expression when x=3 .

$\frac{x+6}{3x + 6}-\frac{x}{4(x+2)}$

Possible Answers:

$\frac{5}{12}$

$\frac{1}3{}$

$\frac{9}{20}$

$\frac{3}{20}$

$\frac{1}2{}$

Correct answer:

$\frac{9}{20}$

Explanation:

We can replace each instance of in the original expression with 3.

$\frac{x+6}{3x + 6}-\frac{x}{4(x+3)}\rightarrow\frac{(3)+6}{3(3)+6}-\frac{(3)}{4[(3)+2]}$

Start by simplifying our numerators and denominators.

$\frac{(3)+6}{3(3)+6}-\frac{(3)}{4[(3)+2]}$

$\frac{9}{9+6}-\frac{3}{4(5)}$

$\frac{9}{15}-\frac{3}{20}$

In order to subtract our fractions, a common denominator must be found. The least common multiple of 15 and 20 is 60.

$15\cdot 4=60$

$20\cdot 3=60$

Multiply both the numerator and denominator of the first fraction by 4, and the second by 3.

$\frac{9\cdot 4}{15\cdot 4}-\frac{3\cdot 3}{20\cdot 3}$

$\frac{36}{60}-\frac{9}{60 }$

Now, the fractions can be combined using subtraction:

$\frac{36-9}{60}=\frac{27}{60}$

Simplify the fraction to find the final answer:

$\frac{27\div3}{60\div3}=\frac{9}{20}$

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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #132 : Polynomials

Example Question #37 : Product Rule Of Exponents

Example Question #541 : Pre Algebra

Example Question #39 : Product Rule Of Exponents

Example Question #542 : Pre Algebra

Example Question #543 : Pre Algebra

Example Question #42 : Product Rule Of Exponents

Example Question #544 : Pre Algebra

Example Question #545 : Pre Algebra

Example Question #2 : Solving Polynomials

All Pre-Algebra Resources

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