Rational Exponents (The exponent is a fraction)

 $2^{4\ }\$    is the same as

•  $2\ \times\ 2\ \times\ 2\ \times\ 2\ \$    so the answer is 16

•  $2\times4\ \$   so the answer Is 8

 $4^{3\ }$   is the same as

•  $3\ \times\ 4\ \$   so the answer is 12

•  $4\times4\times4\ \$   so the answer is 64

Exponents are an example of 

• Repeated addition of the same number

• Repeated multiplication of the same number

• Multiplication with 2 or more different numbers

 $9^{\frac{1}{2}}$   is the same as

•  $\sqrt{9}\$  so the value is 3

•  $9\ \times\ \frac{1}{2\ }\$  so the value is 4.5

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

 $27^{\frac{1}{3}\ \ }$  is the same as

•  $27\ \times\ \frac{1}{3}\$    so the value is 9

•  $\ ^3\sqrt{27}\$   so the value is 3

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

 $8^{\frac{1}{3}}\ \$    is the same as

•  $\ ^3\sqrt{8}\ \$   so the value is 2

•  $8\ \times\ \frac{1}{3}\$   so the value is  $\ \ \frac{8}{3}\ \$  

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

 $25^{\frac{1}{2}\ }$   is the same as

•  $25\ \div\ 2\$   so the answer is 12.5

•  $\sqrt{25}\$    so the answer is 5

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

 $\sqrt{100}\$    is the same as

•  $100^{\frac{1}{3}}$  

•  $100^{\frac{1}{2}}$  

•  $10\times10$  

•  $\ ^3\sqrt{100}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

 $8^{\frac{2}{3}\ }$   is the same as

•  $\ ^3\sqrt{8^2}\ \ \$    so the answer is 4

•  $8\ \times\frac{2}{3}\ \$    so the answer is    $\frac{16}{3}$  

•  $\ \sqrt{8^3}\ \ \$     so the answer is    $\sqrt{512}$  

•  $\ ^3\sqrt{8}\ \ \$     so the  answer is   2

 $64^{\frac{2}{3}}\ \$  is the same as

•  $\ ^3\sqrt{64^2}\$   so the answer is   8

•  $\ ^3\sqrt{64^2}\ \$    so the answer is  16

•  $\ ^3\sqrt{64^2}\ \$    so the answer is  4  

•  $64\ \times\frac{2}{3}\ \ \$    so the answer is    $\frac{32}{3}$