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SAT Math : Exponential Operations

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Example Questions

Example Question #81 : Exponential Operations

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

Possible Answers:

480

240

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 #13 : How To Add Exponents

Solve for $x$ :

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

Possible Answers:

$9$

$11$

$10$

$6$

$8$

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 : Exponential Operations

Simplify:

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

Possible Answers:

$x^{7}$

$x^{10}$

$x^{2}$

$x^{9}$

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 #3 : Exponential Operations

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

Possible Answers:

y³x¹² + y¹²x⁸ + y²⁴x⁴ + y³x²³

y³x¹² + y⁶x⁸ + y⁴⁵x⁴ + y³x⁸⁸

y³x¹² + y⁶x⁸ + y⁴⁵ + x⁸⁸

2x⁴y⁴ + 7y¹⁵ + 7x²²

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

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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Example Question #5 : Exponential Operations

If $\frac{3^{y - 1}}{3^{-2}} = 27^{y}3^{y}$ , what is the value of ?

Possible Answers:

$\frac{1}{3}$

$\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).

$3^{y-1}*3^2=27^y3^y$

The term on the right can be rewritten, as 27 is equal to 3 to the third power.

$3^{y-1}*3^2=(3^3)^y*3^y$

Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.

$3^{(y-1)+2}=(3)^{3y}*3^y$

$3^{y+1}=3^{3y+y}=3^{4y}$

We now know that the exponents must be equal, and can solve for .

y+1=4y

1=3y

$\frac{1}{3}=y$

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Example Question #83 : Exponential Operations

If $5^2 \times 5^n = 5^{12}$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.

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Example Question #84 : Exponential Operations

Simplify: $3^2\times3^3\times3^{-4}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{9}$

Correct answer:

Explanation:

To determine the value of this expression, it is not necessary to determine the values of each term's power. Instead, since these powers have the same bases and are multiplied, the powers can be added.

$3^2\times3^3\times3^{-4} = 3^{2+3+(-4)} = 3^1=3$

The answer is .

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Example Question #16 : How To Add Exponents

If $y = 5^{a} * 5^{b}$ and a + b = 3 , what is the value of ?

Possible Answers:

125

150

Correct answer:

125

Explanation:

Multiplying two exponents that have the same base is the equivalent of simply adding the exponents.

So $y = 5^{a} * 5^{b}$ is the same as $y = 5^{a + b}$ , and if a + b = 3 , then $y = 5^{3}$ or 125 .

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Example Question #87 : Exponents

Evaluate: 3^x+9^x

Possible Answers:

$3^{3x}$

$3^{x^2}$

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

12^x

Correct answer:

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

Explanation:

The exponents cannot be added unless the both bases are alike and similar bases must be multiplied with each other. Rewrite the nine with a base of three.

9=3^2

Rewrite the expression.

$3^x+9^x= 3^x+3^{2x}$

Do not add the exponents, since similar bases are added and are not multiplied with each other!

The answer is: $3^x+3^{2x}$

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Example Question #84 : Exponential Operations

Simplify:

$x^5y^4z^2 \cdot x^4y^5z^2$

Possible Answers:

$x^{20}y^{20}z^{4}$

x^9y^9z^4

$\frac{x^5y^4z^2 }{x^4y^5z^2}$

$xy^{-1}$

Correct answer:

x^9y^9z^4

Explanation:

When we multiply two polynomials with exponents, we add their exponents together. Therefore,

$x^5y^4z^2 \cdot x^4y^5z^2 = x^9y^9z^4$

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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #81 : Exponential Operations

Example Question #13 : How To Add Exponents

Example Question #82 : Exponential Operations

Example Question #3 : Exponential Operations

Example Question #5 : Exponential Operations

Example Question #83 : Exponential Operations

Example Question #84 : Exponential Operations

Example Question #16 : How To Add Exponents

Example Question #87 : Exponents

Example Question #84 : Exponential Operations

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