Rational Exponents

Presentation

•

Mathematics

•

9th Grade

•

Medium

•

CCSS

HSN.RN.A.2, 8.EE.A.2

Standards-aligned

Layan Diab

Used 435+ times

FREE Resource

5 Slides • 13 Questions

Rational Exponents

Fractional Exponents. A rational exponent represents both an integer exponent and an nth root.

Multiple Choice

Complete this sentence: To find the value of a number raised to the $\frac{1}{2}$ power, find the ______ of the number.

Example:

49^{\frac{1}{2}}=?

Square Root

2nd Power

nth root

Square Root

A square root of a number is a value that can be multiplied by itself to give the original number.

A square root of 49 is 7, because when 7 is multiplied by itself we get 49.

Multiple Choice

For any real number b, $b^{\frac{1}{2}}=$

$\sqrt{b}$

$b^2$

$2^b$

Multiple Select

Pick all the right answers:
$64^{\frac{1}{2}}=$

$\sqrt{64}$

$8$

$8^2$

$64$

Multiple Select

Pick all the right answers:
$\sqrt{25}=$

$5$

$\sqrt{5^2}$

$25^{\frac{1}{2}}$

$25$

Multiple Choice

$10^{\frac{1}{2}}=$

$5$

$\sqrt{10}$

$\sqrt{5^2}$

Multiple Choice

$2g^{\frac{1}{2}}\ =\$

$\sqrt{2g}$

$2\sqrt{g}$

$\sqrt{g}$

$g$

Multiple Select

Pick all the right answers:

$\sqrt{16p}\ =\$

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

$\left(4p\right)^{\frac{1}{2}}$

$\left(16p\right)^{\frac{1}{2}}$

$4p$

$4\sqrt{p}$

nth root

This is read as the 5th root of 18

nth Roots

For any real numbers a and b and positive integer n: $a^n\ =\ b$ then $a\ =\ ^n\sqrt{b}$

Example:

5^3\ =\ 125\

then

5\ =\ ^3\sqrt{125}\ =\ \left(125\right)^{\frac{1}{3}}

Simplify

1) $16^{\frac{3}{2}}=\left(^2\sqrt{16}\right)^3=\ ^2\sqrt{16^3}=$

\ ^2\sqrt{4096}=4096^{\frac{1}{2}}=64

8^{\frac{5}{3}}=^3\sqrt{8^5}=^3\sqrt{32768}\ =

^3\sqrt{32^3}=\ 32

Multiple Choice

Write in radical form: $17^{\frac{1}{3}}$

$\ ^3\sqrt{17^1}$

$\ ^1\sqrt{17^3}$

$\ ^2\sqrt{17^3}$

Multiple Choice

Write in radical form:

m^{\frac{2}{3}}

$\ ^3\sqrt{m^2}$

$\ ^2\sqrt{m^3}$

Multiple Choice

Write in exponential form:

\ ^5\sqrt{h}

$h^{\frac{1}{5}}$

$h^{\frac{5}{1}}$

$h^{\frac{5}{2}}$

$h^{\frac{2}{5}}$

Multiple Choice

Write in exponential form:
$\ ^3\sqrt{y^5}$

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

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

Multiple Choice

Evaluate: $\ ^5\sqrt{243}$

Hint: Get the prime factorization of 243.

$3$

$5$

$9\sqrt{3}$

Multiple Choice

if $y^{\frac{1}{3}}=\ 10\$ then what is the value of y?

1,000

0.001

Rational Exponents

Fractional Exponents. A rational exponent represents both an integer exponent and an nth root.

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