Indices - including fractional and negative

Simplify fully  $x^3\times x^7=?$  

•  $x^{21}$  

•  $x^{10}$  

•  $x^4$  

• None of these

Simplify fully  $x^5\times x^{-2}=?$  

•  $x^3$  

•  $x^7$  

•  $x^{10}$  

•  $x^{-10}$  

How else could you write  $4^{-2}$  ?

•  $16$  

•  $-16$  

•  $-\frac{1}{16}$  

•  $\frac{1}{16}$  

Tags

CCSS.HSN.RN.A.2

 $\frac{2}{x^3}=?$  

•  $2x^3$  

•  $2x^{-3}$  

•  $8x^3$  

•  $8x^{-3}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Which of the following is equivalent to the expression  $\frac{1}{2x^7}$  ?

•  $\left(2x\right)^{-7}$  

•  $\frac{1}{2}x^7$  

•  $\frac{1}{2}x^{-7}$  

•  $2x^{-7}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

How else can you write  $\sqrt{x}$  ?

•  $x^{\frac{1}{2}}$  

•  $x^2$  

•  $x^{-2}$  

•  $x^{\frac{1}{4}}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Which of the following is equivalent to  $x^{\frac{2}{3}}$  ?

•  $3\sqrt{x^2}$  (cube root of x squared)

•  $\sqrt{x^3}$  (square root of x cubed)

•  $x^6$  

• None of these

Which expression below is equivalent to  $3x^5+5\sqrt{x}-\frac{7}{x^3}$  ?

•  $3x^5-5x^2-7x^{-3}$  

•  $3x^5-5x^2+7x^3$  

•  $3x^5+5x^{-2}-7x^{-3}$  

•  $3x^5+5x^{\frac{1}{2}}-7x^{-3}$  

Simplify the following  $3x^7\times2\sqrt{x}\times\frac{5}{x^3}$  

•  $30x^2$  

•  $30x^{\frac{21}{2}}$  

•  $30x^{\frac{9}{2}}$  

•  $30x^{\frac{7}{2}}$  

Which of the following is equivalent to this expression  $2x^3\times4\sqrt{x^3}\times\frac{5}{2x^5}$  ?

•  $20x^{-\frac{1}{2}}$  

•  $80x^2$  

•  $80x^{-\frac{1}{2}}$  

• none of the above