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ACT Math : Exponents

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Example Questions

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Example Question #71 :Exponents

If $x^{\frac{5}{2}} = 1024$ , what is?

Possible Answers:

Correct answer:

Explanation:

Using the properties of exponents, we can raise both sides to a reciprocal of the exponent ofto find the value we need. Specifically...

$x^{\frac{5}{2}} = 1024$

$(x^{\frac{5}{2}})^{\frac{2}{5}} = 1024^{\frac{2}{5}}$

$x = 1024^{\frac{2}{5}} = (\sqrt[5]{1024})^{2} = 4^2 = 16$

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例子问题# 72:Exponents

Simplify:

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

Possible Answers:

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

$x^{2}$

Correct answer:

Explanation:

When exponents with the same base are being divided, you may substract the exponent in the denominator from the exponent in the numerator to create a new exponent. In this case, you would subtractfrom, yieldingas the new exponent. Keeping the same base, the answer becomes.

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Example Question #73 :Exponents

What is the simplified form for the following expression?

$\frac{(2xz^2)^3}{(4zx^2)^2}$

Possible Answers:

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

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

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

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

2*z^3*x^3

Correct answer:

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

Explanation:

Break up by variable.

$\frac{2^3}{4^2}= \frac{1}{2}$

$\frac{x^3}{x^4}= \frac{1}{x}$

$\frac{z^6}{z^2} = z^4$

Therefore the simplified form becomes,

$\frac{(2xz^2)^3}{(4zx^2)^2}=\frac{z^4}{2x}$ .

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Example Question #74 :Exponents

$64^{\frac{4}{3}}$ can be written as which of the following?

A. $\sqrt[3]{64^4}$

B。 $(\sqrt[3]{64})^{4}$

C. 256

Possible Answers:

B only

C only

A, B and C

A and C

B and C

Correct answer:

A, B and C

Explanation:

C is computing the exponent, while A and B are equivalent due to properties of fractional exponents.

Remember that...

$a^{\frac{b}{c}} = \sqrt[c]{a^b} = (\sqrt[c]{a})^b$

$64^{\frac{4}{3}}=$ $\sqrt[3]{64^4}=$ $(\sqrt[3]{64})^{4}=$ 256

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Example Question #3 :Exponential Operations

$\dpi{100} \small \frac{7^{10}-7^{8}}{7^{9}-7^{7}}=$

Possible Answers:

$\dpi{100} \small 343$

$\dpi{100} \small 7$

$\dpi{100} \small 42$

$\dpi{100} \small 28$

$\dpi{100} \small 49$

Correct answer:

$\dpi{100} \small 7$

Explanation:

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is 7^7 .

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}$

Now, we can cancel out the 7^7 from the numerator and denominator and continue simplifying the expression.

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}=\frac{7^3-7^1}{7^2-1}=\frac{343-7}{49-1}=\frac{336}{48}=7$

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Example Question #1 :How To Use Foil With Exponents

For all $x,\ (5x+2)^{2}=$ ?

Possible Answers:

$25x^{2}+20x+4$

$25x^{2}+10x+4$

$25x^{2}+4$

$10x^{2}+4$

$10x+4$

Correct answer:

$25x^{2}+20x+4$

Explanation:

$(5x+2)^{2}$ 相当于 $(5x+2)(5x+2)$ .

Using the FOIL method, you multiply the first number of each set $5x\cdot 5x=25x^{2}$ , multiply the outer numbers of each set $5x\cdot 2=10x$ , multiply the inner numbers of each set $2\cdot 5x=10x$ , and multiply outer numbers of each set $2\cdot 2=4$ .

Adding all these numbers together, you get $25x^{2}+10x+10x+4=25x^{2}+20x+4$ .

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Example Question #1 :Exponents And The Distributive Property

$(4x-9)^{3}=?$

Possible Answers:

12x^3-27

12x-27

64x^3-729

64x^3-432x^2+972x-729

Correct answer:

64x^3-432x^2+972x-729

Explanation:

FOIL the first two terms:

(4x-9)(4x-9)=16x^2-36x-36x+81 = 16x^2-72x+81

Next, multiply this expression by the last term:

(16x^2-72x+81)(4x-9)=64x^3-144x^2-22x^2+648x+324x-729

Finally, combine the terms:

(4x-9)^3=64x^3-432x^2+972x-729

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Example Question #3 :How To Use Foil With Exponents

If q=2 , what is the value of the equation $q(q-7)^{2}$ ?

Possible Answers:

100

Correct answer:

Explanation:

Plug inforin the equation $q(q-7)^{2}$

That gives: $2(2-7)^{2}$

Then solve the computation inside the parenthesis: $2(-5)^{2}$

The answer should then be

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Example Question #4 :How To Use Foil With Exponents

The expression (4x^3-2)(9x^6+7) 相当于__________.

Possible Answers:

9x^9-2x^6+7x^3-14

4x^9-18x^6+28x^3-14

36x^9-18x^6-28x^3+14

36x^9-18x^6+28x^3-14

$36x^{18}-18x^6+28x^3-14$

Correct answer:

36x^9-18x^6+28x^3-14

Explanation:

使用FOIL and be mindful of exponent rules. Remember that when you multiply two terms with the same bases but different exponents, you will need to add the exponents together.

Foilexpo

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Example Question #5 :How To Use Foil With Exponents

The expression (3x^2+x)(4x^3+2x) 相当于__________.

Possible Answers:

12x^6+4x^3+6x^2+2x

12x^5+4x^4+8x^2

12x^5+4x^4+6x^3+2x^2

12x^5+10x^4+6x^3+2x^2

12x^5+4x^4+6x^3+6x^2

Correct answer:

12x^5+4x^4+6x^3+2x^2

Explanation:

Remember to add exponents when two terms with like bases are being multiplied.

Foilexpo

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ACT Math : Exponents

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #71 :Exponents

例子问题# 72:Exponents

Example Question #73 :Exponents

Example Question #74 :Exponents

Example Question #3 :Exponential Operations

Example Question #1 :How To Use Foil With Exponents

Example Question #1 :Exponents And The Distributive Property

Example Question #3 :How To Use Foil With Exponents

Example Question #4 :How To Use Foil With Exponents

Example Question #5 :How To Use Foil With Exponents

All ACT Math Resources

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