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SAT Math : Exponents

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Example Question #691 : Algebra

What is the unit's digit of $2^{357}$ ?

Possible Answers:

Correct answer:

Explanation:

Notice that there is a repeating pattern in the unit's digit of the powers of 2:

2^1=2

2^2=4

2^3=8

2^4=16

2^5=32

2^6=64

and so on. The pattern is four numbers long, which means we need to count how many complete blocks of 4 numbers are in the 357-number pattern. That is,

$357\div4=89$ with a remainder of 1.

The remainder is all we need, since it tells us where in the pattern we need to be: the first place, with a unit's digit of 2.

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Example Question #1161 : Algebra

If (x-3)^2=25 , which of the following could be the value of ?

Possible Answers:

Correct answer:

Explanation:

(x-3)^2=25

Take the square root of both sides.

$x-3=\pm 5$

$x-3=5\ \text{or}\ x-3=-5$

Add 3 to both sides of each equation.

$x=5+3\ \text{or}\ x=-5+3$

$x=8\ \text{or}\ x=-2$

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Example Question #1161 : Algebra

Simplify:

$\left ( xyz \right )^{3}+x^{2}y+\left ( xy \right )^{0}+\left ( xy^{\frac{1}{2}} \right )^{2}$

Possible Answers:

$x^{3}y^{3}z^{3}+2x^{2}y$

$x^{3}y^{3}z^{3}+2x^{2}y+1$

$x^{3}y^{3}z^{3}+x^{2}y+1$

$2x^{5}y^{3}z$

$x^{3}y^{3}z^{3}+x^{2}y$

Correct answer:

$x^{3}y^{3}z^{3}+2x^{2}y+1$

Explanation:

$\left ( xyz \right )^{3}+x^{2}y+\left ( xy \right )^{0}+\left ( xy^{\frac{1}{2}} \right )^{2}$

= x³y³z³ + x²y + x⁰y⁰ + x²y

= x³y³z³ + x²y + 1 + x²y

= x³y³z³ + 2x²y + 1

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Example Question #1161 : Algebra

Use the FOIL method to simplify the following expression:

(x^3+2x^2)^2

Possible Answers:

4x^5+4

5x^6+4x^4

x^6+4x^4

x^6+4x^5+4x^4

x^6+2x^4

Correct answer:

x^6+4x^5+4x^4

Explanation:

Use the FOIL method to simplify the following expression:

(x^3+2x^2)^2

Step 1: Expand the expression.

(x^3+2x^2)(x^3+2x^2)

Step 2: FOIL

First: $x^3\cdot x^3 = x^6$

Outside: $x^3 \cdot 2x^2 =2x^5$

Inside: $2x^2 \cdot x^3 = 2x^5$

Last: $2x^2 \cdot 2x^2 = 4x^4$

Step 2: Sum the products.

x^6+2x^5+2x^5+4x^4

x^6+4x^5+4x^4

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Example Question #1 : Exponents And The Distributive Property

Square the binomial.

$(x^{2}y^{4}+xy^{6})^{2}$

Possible Answers:

$x^4y^{16}+2x^2y^{24}+xy^{36}$

$2x^{8}y^{20}$

$x^8y^8+x^2y^{12}$

$x^4y^8+2x^3y^{10}+x^2y^{12}$

$x^{4}y^{8}+x^{2}y^{12}$

Correct answer:

$x^4y^8+2x^3y^{10}+x^2y^{12}$

Explanation:

$(x^{2}y^{4}+xy^{6})^{2}$

$(x^{2}y^{4}+xy^{6})(x^{2}y^{4}+xy^{6})$

We will need to FOIL.

First: x^2y^4*x^2y^4=x^4y^8

Inside: $xy^6*x^2y^4=x^3y^{10}$

Outside: $x^2y^4*xy^6=x^3y^{10}$

Last: $xy^6*xy^6=x^2y^{12}$

Sum all of the terms and simplify.

$x^4y^8+x^3y^{10}+x^3y^{10}+x^2y^{12}$

$x^4y^8+2x^3y^{10}+x^2y^{12}$

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Example Question #1161 : Algebra

Which of the following is equivalent to 4c(3d)³– 8c³d + 2(cd)⁴?

Possible Answers:

2(54d²– 4c²+ 2c³* d³)

cd(54c * d³– 4c³+ c²* d²)

None of the other answers

2cd(54d² – 4c²+ c³* d³)

Correct answer:

2cd(54d² – 4c²+ c³* d³)

Explanation:

First calculate each section to yield 4c(27d³) – 8c³d + 2c⁴d⁴= 108cd³– 8c³d + 2c⁴d⁴. Now let's factor out the greatest common factor of the three terms, 2cd, in order to get: 2cd(54d²– 4c²+ c³d³).

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SAT Math : Exponents

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #691 : Algebra

Example Question #1161 : Algebra

Example Question #1161 : Algebra

Example Question #1161 : Algebra

Example Question #1 : Exponents And The Distributive Property

Example Question #1161 : Algebra

All SAT Math Resources

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