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ACT Math : Exponential Operations

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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 of to 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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Example Question #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 subtract from , yielding as 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 #151 : Exponents

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

Possible Answers:

$\dpi{100} \small 28$

$\dpi{100} \small 42$

$\dpi{100} \small 7$

$\dpi{100} \small 343$

$\dpi{100} \small 49$

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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ACT Math : Exponential Operations

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #71 : Exponents

Example Question #72 : Exponents

Example Question #73 : Exponents

Example Question #74 : Exponents

Example Question #151 : Exponents

All ACT Math Resources

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