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ACT Math : Algebra

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Example Questions

Example Question #21 : How To Multiply Exponents

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

Possible Answers:

2(a^5+b^5)

(a^2+b^2)^5

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

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

None of these

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 #721 : Algebra

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

Possible Answers:

$x^{15}$

$x^{25}$

$x^{10}$

$x^{225}$

$x^{5}$

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 #722 : Algebra

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

Possible Answers:

$25^{4}$

$10^{2}$

$5^{4}$

$25^{2}$

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 #723 : Algebra

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

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

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

Possible Answers:

C only

A and C

B and C

A only

A, 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 #724 : Algebra

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

Possible Answers:

1024

1000

4096

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 #725 : Algebra

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

Possible Answers:

$x^{2}$

$x^{10}$

$x^{32}$

$x^{24}$

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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Example Question #726 : Algebra

Simplify: $(y^{3})^{4}$

Possible Answers:

$y^{7}$

$4y^{3}$

$y^{\frac{3}{4}}$

$y^{12}$

Correct answer:

$y^{12}$

Explanation:

When an exponent is raised to an exponent, multiply the two together to yield a new exponent, and attach that exponent to the original base.

In this case, multiply and to yield , and your answer is $y^{12}$ .

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Example Question #32 : Exponential Operations

Solve: $(x^{2})^{2}$ when x=4 .

Possible Answers:

256

Correct answer:

256

Explanation:

When an exponent is raised to another exponent, you may multiply them together to find the exponent of the answer. Attach that exponent to the original base, and that is the solution.

In this particular problem, multiply by , which yields as the final exponent. This makes $x^{4}$ .

Now, substitute for : $4^{4}=256$ .

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : How To Multiply Exponents

Example Question #721 : Algebra

Example Question #722 : Algebra

Example Question #723 : Algebra

Example Question #21 : How To Multiply Exponents

Example Question #724 : Algebra

Example Question #725 : Algebra

Example Question #21 : Exponential Operations

Example Question #726 : Algebra

Example Question #32 : Exponential Operations

All ACT Math Resources

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