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ACT Math : Exponential Operations

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Example Questions

Example Question #21 : Exponential Operations

Simplify

x^4y^2(3x^4+2yx^2 + 5y) .

Possible Answers:

3x^8y^2 + 7x^4y^3

3x^16+2x^8y^2 + 5x^4y^2

3x^16y^2+2x^8y^2 + 5x^4y^2

3x^8y^2+2x^6y^3 + 5x^4y^3

10x^18y^8

Correct answer:

3x^8y^2+2x^6y^3 + 5x^4y^3

Explanation:

This is just a matter of simply distributing this multiplication. Start by the basic distribution:

x^4y^2(3x^4+2yx^2 + 5y) = 3x^4*x^4y^2+2yx^2*x^4y^2 + 5y*x^4y^2

Now, you just add the exponents that are similar. Thus, you get:

3x^8y^2+2x^6y^3 + 5x^4y^3

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Example Question #21 : How To Multiply Exponents

Simplify the following:

$(a^{x+n})\cdot(a^{x-n})$

Possible Answers:

$a^{x^{2}-n^{2}}$

$(a^{2})^{x^{2}-n^{2}}$

$a^{2x}$

None of these

$\frac{a^{n^{2}}}{a^{x^{2}}}$

Correct answer:

$a^{2x}$

Explanation:

The rule for multiplying exponents is

$a^m \cdot a^n = a^{m+n}$ .

Using this, we see that

$(a^{x+n})\cdot(a^{x-n}) = a^{((x+n)+(x-n))} = a^{2x}$ .

Thus, our answer is $a^{2x}$ .

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Example Question #22 : Exponents

The expression $a^{10}+b^{10}$ is equivalent to which of the following?

Possible Answers:

None of these

((a^5)^2)+((b^2)^5)

2(a^5+b^5)

(a^2+b^2)^5

$\frac{(a^{20}+b^{20})}{2}$

Correct answer:

((a^5)^2)+((b^2)^5)

Explanation:

The formula for multiplying exponents is

$a^m \cdot a^n=a^{m+n}$ .

Using this, we see that

$((a^5)^2) = a^5 \cdot a^5 = a^{10}$ , and

$(b^2)^5=b^2 \cdot b^2 \cdot b^2 \cdot b^2 \cdot b^2 = b^{10}$ .

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Example Question #21 : Exponential Operations

Simplify the following: $x^{5}\cdot x^{5}$

Possible Answers:

$x^{10}$

$x^{25}$

$x^{225}$

$x^{15}$

$x^{5}$

Correct answer:

$x^{10}$

Explanation:

When two variables with exponents are multiplied, you can simplify the expression by adding the exponents together. In this particular problem, the correct answer is found by adding the exponents 5 and 5, yielding $x^{10}$ .

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Example Question #22 : Exponential Operations

Simplify the following to its simplest exponential expression: $5^{2}\cdot5^{2}$

Possible Answers:

$25^{2}$

$10^{2}$

$5^{4}$

$25^{4}$

Correct answer:

$5^{4}$

Explanation:

When multiplying exponential expressions, the bases remain the same and the exponents are added. Thus, the answer to this question is $5^{4}$ .

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Example Question #23 : Exponential Operations

$2^{6}$ can be written as which of the following?

A. $(2^{3})^{2}$

B. $\frac{1}{2^{-5}}$

Possible Answers:

A, B and C

A and C

C only

A only

B and C

Correct answer:

A and C

Explanation:

B is not equivalent because...

$\frac{1}{2^{-5}} = 2^{5} = 32$

A is equivalent because of a property of exponents meaning that $(a^b)^c = a^{bc}$ . Consequently,

$(2^{3})^{2} = 2^{6}$

C is simply computing $2^{6} = 32$ .

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Example Question #21 : How To Multiply Exponents

Solve $3x^{3}+2y$ when x=2 and y=4 .

Possible Answers:

Correct answer:

Explanation:

Substitute for and for : $3(2^{3})+2(4)$

Simplify: 3(8)+8

24+8=32

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Example Question #24 : Exponential Operations

What is $(4^{3})^{2}$ ?

Possible Answers:

4096

1024

1000

1600

Correct answer:

4096

Explanation:

When an exponent is raised to an exponent, you may simplify by multiplying the exponents together to make a new exponent. In this case, $(4^{3})^{2}$ becomes $4^{6}$ , which equals 4096 .

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Example Question #25 : Exponential Operations

Simplify: $x^{6}(x^{4})$

Possible Answers:

$x^{32}$

$x^{10}$

$x^{24}$

$x^{2}$

Correct answer:

$x^{10}$

Explanation:

When exponents with the same base are being multiplied, you may add the exponents together to create a new exponent.

In this case, you would add 6 and 4 to create 10 as the new exponent.

Keeping the same base, the answer becomes $x^{10}$ .

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Example Question #21 : Exponential Operations

Solve: $3x^{4}-2y^{2}$ when x=2 and y=1 .

Possible Answers:

Correct answer:

Explanation:

Substitute for and for : $3(2^{4})-2(1^{2})$ .

Simplify: 3(16)-2

48-2=46

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ACT Math : Exponential Operations

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : Exponential Operations

Example Question #21 : How To Multiply Exponents

Example Question #22 : Exponents

Example Question #21 : Exponential Operations

Example Question #22 : Exponential Operations

Example Question #23 : Exponential Operations

Example Question #21 : How To Multiply Exponents

Example Question #24 : Exponential Operations

Example Question #25 : Exponential Operations

Example Question #21 : Exponential Operations

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