LAWS OF EXPONENTS FOR RATIONAL EXPONENTS

Which of the following CORRECTLY illustrates power of a power rule for rational exponents?

• (m^1/2)^1/3 = m^1/5

• (n^2/3)^1/3 = n¹

• (q^3/5)^1/5 = q^4/5

• (p^2/3)^2/5 = p^4/15

Which among the following is the correct exponent for the product of the expression  $g^{\frac{2}{7}}\times g^{\frac{1}{3}}=g^?$  

•  $\frac{13}{21}$  
  

•  $-\frac{1}{21}$  

•  $\frac{2}{21}$  

•  $\frac{6}{7}$  

Which of the following is the simplified form of the expression  $\frac{k^{\frac{5}{6}}}{k^{\frac{2}{6}}}$ ?

•  $k^{\frac{1}{6}}$  

•  $k^{\frac{1}{2}}$  

•  $k^{\frac{1}{3}}$  

•  $k^{\frac{7}{6}}$  

Which among the following correctly illustrates the power of a product rule for rational exponents?

• $\left(2a^{\frac{1}{4}}b^{\frac{3}{5}}\right)^{\frac{1}{2}}=2^{\frac{1}{2}}a^{\frac{1}{8}}b^{\frac{3}{10}}$

• $\left(2a^{\frac{1}{4}}b^{\frac{3}{5}}\right)^{\frac{1}{2}}=2a^{\frac{1}{6}}b^{\frac{4}{7}}$

• $\left(2a^{\frac{1}{4}}b^{\frac{3}{5}}\right)^{\frac{1}{2}}=2^{\frac{1}{2}}a^{\frac{3}{4}}b^{\frac{11}{10}}$

• $\left(2a^{\frac{1}{4}}b^{\frac{3}{5}}\right)^{\frac{1}{2}}=\frac{2a}{b^2}$

Power of a power rule states that whenever an exponential expression is raised to another power, we simply (a)   the exponents.

Which of the following is the simplified form of the expression  $6q^{-5}$ ?

•  $\frac{1}{6q^5}$  

•  $\frac{6}{q^{-5}}$  

•  $\frac{1}{6q^{-5}}$  

•  $\frac{6}{q^5}$  

Which of the following statements is TRUE about zero exponents rule?

• Any nonzero expression raised to zero is equal to the expression itself.

• Any nonzero expression raised to zero is equal to 1.

• Any nonzero expression raised to zero is equal to 0.

• Any nonzero expression raised to zero is equal to its reciprocal.

Simplify:  $\frac{8b^3c^5d^7}{4b^2c^5d^9}$  

•  $\frac{2d^2}{b}$  

•  $\frac{2b}{d^2}$  

•  $\frac{b}{2d^2}$  

•  $2bd^2$  

Which among the following is the simplified form of the expression  $\frac{48s^{-2}t^{-3}}{8u^4v^{-5}}$ ?

•  $\frac{6s^2t^3}{u^4v^5}$  

•  $\frac{6}{s^2t^3u^4v^5}$  

•  $\frac{6v^5}{s^2t^3u^4}$  

•  $6s^2t^3u^4v^5$  

 $\frac{\left(h^{\frac{1}{3}}\right)^{\frac{1}{2}}}{h^5}$  

What two laws of exponents can be used to simplify the expression:

• Power of a  Product

• Quotient of Powers

• Power of a Power

• Product of Powers