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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #5 : How To Add Exponents

Simplify. All exponents must be positive.

$\left ( x^{-2}y^{3} \right )\left ( x^{5}y^{-4} \right )$

Possible Answers:

$\left ( x^{-2}+x^{5} \right )\left ( y^{3}+y^{-4} \right )$

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

$x^{7}y^{7}$

$\frac{x^{3}}{y}$

$x^{2}y^{7}$

Correct answer:

$\frac{x^{3}}{y}$

Explanation:

Step 1: $\left ( x^{-2}x^{5} \right )= x^{3}$

Step 2: $\left ( y^{3}y^{-4} \right )= y^{-1}= \frac{1}{y}$

Step 3: (Correct Answer): $\frac{x^{3}}{y}$

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Example Question #6 : How To Add Exponents

Simplify. All exponents must be positive.

$\frac{x^{-3}y^{5}}{x^{2}y^{-1}}$

Possible Answers:

$\frac{y^{6}}{x^{5}}$

$x^{-5}y^{6}$

$x^{-1}y^{4}$

$\frac{1}{x^{5}y^{-6}}$

$\frac{\left ( xy \right )^{2}}{\left ( xy \right )}$

Correct answer:

$\frac{y^{6}}{x^{5}}$

Explanation:

Step 1: $\frac{y^{5}}{\left ( x^{3}x^{2} \right )\left \right )y^{-1}}$

Step 2: $\frac{\left ( y^{5}y^{1} \right )}{x^{3}x^{2}}$

Step 3: $\frac{y^{6}}{x^{5}}$

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Example Question #7 : How To Add Exponents

$\frac{\left ( -11 \right )^{-8}}{\left ( -11\right )^{12}}$

Answer must be with positive exponents only.

Possible Answers:

$\frac{1}{\left ( -11 \right )^{20}}$

$\left ( 1 \right )^{-20}$

$\frac{1}{\left ( -11 \right )^{4}}$

$\left ( -11 \right )^{-20}$

$\left ( -11 \right )^{4}$

Correct answer:

$\frac{1}{\left ( -11 \right )^{20}}$

Explanation:

Step 1: $\frac{1}{\left ( -11 \right )^{12}\left ( -11 \right )^{8}}$

Step 2: The above is equal to $\frac{1}{\left ( -11 \right )^{20}}$

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Example Question #74 : Exponents

Evaluate:

$-\left ( -3 \right )^{0}-\left ( -3^{0} \right )$

Possible Answers:

Correct answer:

Explanation:

$-\left ( -3 \right )^{0}= -1$

$(-3^{0})=-1$

-1-(-1)=-1+1=0

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Example Question #9 : How To Add Exponents

Simplify:

$3\sqrt{18} + 2\sqrt{50}$

Possible Answers:

$5\sqrt{68}$

$None\ of\ the\ above$

$10\sqrt{2}$

$19\sqrt{2}$

$9\sqrt{2}$

Correct answer:

$19\sqrt{2}$

Explanation:

$3\sqrt{18} = 3\sqrt{2\star 3^{2}} = 9\sqrt{2}$

Similarly $2\sqrt{50} = 2\sqrt{2\star 5^{2}} = 10\sqrt{2}$

So $9\sqrt{2} + 10\sqrt{2}= 19\sqrt{2}$

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Example Question #1 : How To Add Exponents

If $3^{4x+6}=27^{2x}$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Using exponents, 27 is equal to 3³. So, the equation can be rewritten:

3^{4x + 6} = (3³)^2x

3^{4x + 6} = 3^6x

When both side of an equation have the same base, the exponents must be equal. Thus:

4x + 6 = 6x

6 = 2x

x = 3

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Example Question #81 : Exponents

What is the value of such that 2^n=4^2*16^3*32^2 ?

Possible Answers:

240

480

Correct answer:

Explanation:

We can solve by converting all terms to a base of two. 4, 16, and 32 can all be expressed in terms of 2 to a standard exponent value.

$4=2^2\rightarrow 4^2=(2^2)^2$

$16=2^4\rightarrow 16^3=(2^4)^3$

$32=2^5\rightarrow 32^2=(2^5)^2$

We can rewrite the original equation in these terms.

2^n=(2^2)^2*(2^4)^3*(2^5)^2

Simplify exponents.

$2^n=(2^4)*(2^{12})*(2^{10})$

Finally, combine terms.

$2^n=2^{4+12+10}=2^{26}$

From this equation, we can see that n=26 .

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Example Question #82 : Exponents

Solve for $x$ :

$4^{4}+4^{4}+4^{4}+4^{4}=2^{x}$

Possible Answers:

$10$

$9$

$11$

$6$

$8$

Correct answer:

$10$

Explanation:

Combining the powers, we get $1024=2^{x}$ .

From here we can use logarithms, or simply guess and check to get $x=10$ .

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Example Question #82 : Exponents

Simplify:

$x^{4}\cdot x^{5}$

Possible Answers:

$x^{9}$

$x^{10}$

$x^{2}$

$x^{7}$

Correct answer:

$x^{9}$

Explanation:

When multiplying exponents with the same base, we use the rules of exponents.

This means you must simply add the exponents together as shown below:

$x^{4}\cdot x^{5} = x^{4+5} = x^{9}$

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Example Question #6 : Exponential Operations

Simplify: y³x⁴(yx³ + y²x² + y¹⁵ + x²²)

Possible Answers:

y³x¹² + y⁶x⁸ + y⁴⁵ + x⁸⁸

2x⁴y⁴ + 7y¹⁵ + 7x²²

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

y³x¹² + y¹²x⁸ + y²⁴x⁴ + y³x²³

y³x¹² + y⁶x⁸ + y⁴⁵x⁴ + y³x⁸⁸

Correct answer:

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

Explanation:

When you multiply exponents, you add the common bases:

y⁴ x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #5 : How To Add Exponents

Example Question #6 : How To Add Exponents

Example Question #7 : How To Add Exponents

Example Question #74 : Exponents

Example Question #9 : How To Add Exponents

Example Question #1 : How To Add Exponents

Example Question #81 : Exponents

Example Question #82 : Exponents

Example Question #82 : Exponents

Example Question #6 : Exponential Operations

All SAT Math Resources

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