Exponent Rules

Project ID: 
7100020027
Accepted: 
Type: 
Layout: 
Question: 
Match the expressions that are equal for all positive real numbers $x$ and $y$.
Question 1: 
$\left( x^2\right)^3$
Answer 1: 
$x^6$
Question 2: 
$x^{-\frac14} \cdot x^{\frac34}$
Answer 2: 
$x^{\frac12}$
Question 3: 
$\left( x^{-\frac12}\right)^{-2}$
Answer 3: 
$x$
Question 4: 
$\frac{x^{-\frac25}}{x^{\frac35}}$
Answer 4: 
$x^{-1}$
Question 5: 
$x^5 \cdot y^5$
Answer 5: 

$(xy)^5$

Question 6: 
$\frac{x^3}{y^3}$
Answer 6: 
$\left( \frac{x}{y}\right)^3$
Question 7: 
$\left(\frac1{x} \right)^{-2}$
Answer 7: 
$x^2$
Question 8: 
$2^{-1} \cdot \frac{4}{x^{-2}}$
Answer 8: 
$2x^2$
Question 9: 
$\left[ \left(2^0 \cdot x^{-2}\right)^{-2}\right]^{-2}$
Answer 9: 
$x^{-8}$