Integer Exponents

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College Algebra › Integer Exponents

Questions 1 - 10

1

Evaluate

$X^{14}$

$X^{48}$

$X^{2}$

Explanation

When like terms with exponents are multiplied, you add the exponents.

$X^8*X^6 = X^{8+6} = X^{14}$

2

$\sqrt[5]{x^{10}}=$

$x^{50}$

$x^{15}$

$10x^{5}$

Explanation

The root of is . Thus

$\sqrt[5]{x^{10}}=x^{10/5}=x^2$

3

$x^{10}$

$x^{-3}$

$x^{7}$

Explanation

When a term with an exponent is raised to another power, multiply the exponents. Thus

$(x^2)^5=x^{2*5}=x^{10}$

4

Evaluate the following:

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

$x^{6}$

$x^{8}$

$x^{2}$

$2x^{4}$

Explanation

When similar terms raised to n are multiplied, simply add the exponents. Thus

$x^{2}*x^{4}=x^{2+4}=x^{6}$

5

$x^{2/3}$

Explanation

When a term with an exponent is raised to another power, multiply the exponents. Thus

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

6

$\sqrt[4]{x^{64}}=$

$x^{16}$

$\frac{x^{64}}{4}$

$x^{68}$

$x^{60}$

$6x^{10}$

Explanation

The root of is $x^{\frac{y}{n}}$ thus

$\sqrt[4]{x^{64}}=x^{64/4}=x^{16}$

7

$x^{24}$

$x^{10}$

$x^{-2}$

$x^{12}$

Explanation

When a term with an exponent is raised to another power, multiply the exponents. Thus

$(x^4)^6=x^{4*6}=x^{24}$

8

$\frac{x^{10}}{x^{6}}=$

$x^{16}$

$x^{60}$

$\frac{x^5}{x^3}$

Explanation

When similar terms raised to n are divided, subtract the exponents. Thus

$\frac{x^{10}}{x^{6}}=x^{10-6}=x^4$

9

$\frac{x^{6}}{x^{3}}=$

$x^{27}$

$x^{12}$

$x^{1/2}$

Explanation

When similar terms raised to n are divided, subtract the exponents. Thus

$\frac{x^{6}}{x^{3}}=x^{6-3}=x^3$

10

$x^{3}*x^{5}=$

$x^{8}$

$x^{5}$

$x^{15}$

$x^{2}$

Explanation

When similar terms raised to n are multiplied, simply add the exponents. Thus

$x^{3}*x^{5}=x^{3+5}=x^{8}$

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