Algebra II U5D5 Rational Exponents Practice

When b > 0 and d is a positive integer, the expression  $\left(3b\right)^{\frac{2}{d}}$  is equivalent to 

•  $\frac{1}{\left(^d\sqrt{3b}\right)^2}$  

•  $\left(\sqrt{3b}\right)^d$  

•  $\frac{1}{\sqrt{3b^d}}$  

•  $\left(^d\sqrt{3b}\right)^2$  

The expression  $\left(\frac{m^2}{m^{\frac{1}{3}}}\right)^{-\frac{1}{2}}$  is equivalent to

•  $-^6\sqrt{m^5}$  

•  $\frac{1}{^6\sqrt{m^5}}$  

•  $-m\ ^5\sqrt{m}$  

•  $\frac{1}{m\ ^5\sqrt{m}}$  

If  $p\left(x\right)\ =\ ab^x$  and  $r\left(x\right)\ =\ cd^x$ , then  $p\left(x\right)\cdot r\left(x\right)$  equals  

•  $ac\left(b+d\right)^x$  

•  $ac\left(b+d\right)^{2x}$  

•  $ac\left(bd\right)^x$  

•  $ac\left(bd\right)^{2x}$  

Tags

CCSS.HSF-IF.C.8B

For  $x\ne0$ , which expressions are equivalent to one divided by the sixth root of x?
I.    $\frac{^6\sqrt{x}}{^3\sqrt{x}}$           II.  $\frac{x^{\frac{1}{6}}}{x^{\frac{1}{3}}}$           III.  $x^{-\frac{1}{6}}$   
 

• I and II, only

• I and III, only

• II and III, only

• I, II, and III

What does  $\left(\frac{-54x^9}{y^4}\right)^{\frac{2}{3}}$  equal?

•  $\frac{9ix^6\cdot^3\sqrt{4}}{y\cdot^3\sqrt{y^2}}$  

•  $\frac{9ix^6\cdot^3\sqrt{4}}{y^2\cdot^3\sqrt{y^2}}$  

•  $\frac{9x^6\cdot\ ^3\sqrt{4}}{y\cdot\ ^3\sqrt{y}}$  

•  $\frac{9x^6\cdot^3\sqrt{4}}{y^2\cdot^3\sqrt{y^2}}$  

For a given time, x, in seconds, an electric current, y, can be represented by  $y=2.5\left(1-2.7^{-.10x}\right)$ . Which equation is not equivalent? 

•  $y=2.5-2.5\left(2.7^{-.10x}\right)$  

•  $y=2.5-2.5\left(\left(2.7^2\right)^{-.05x}\right)$  

•  $y=2.5-2.5\left(\frac{1}{2.7^{.10x}}\right)$  

•  $y=2.5-2.5\left(2.7^{-2}\right)\left(2.7^{.05x}\right)$  

Tags

CCSS.HSF.BF.B.5

If  $n=\sqrt{a^5}$  and  $m=a$  , where  $a>0$  , an expression for  $\frac{n}{m}$  could be 

•  $a^{\frac{5}{2}}$  

•  $a^4$  

•  $^3\sqrt{a^2}$  

•  $\sqrt{a^3}$  

Tags

CCSS.HSN.RN.A.2

For  $x>0$ , which expression is equivalent to  $\frac{^3\sqrt{x^2}\cdot\sqrt{x^5}}{^6\sqrt{x}}$  

•  $x$  

•  $x^{\frac{3}{2}}$  

•  $x^3$  

•  $x^{10}$