Question

Drag expressions to complete each equation.

Answer 1

$a^{-b} =\frac{1}{a^{b}}$

$\frac{a^{b}}{a^{c}} = a^{b-c}$

$\frac{a^{c}}{b^{c}} =(\frac{a}{b} )^{c}$

When you have a negative exponent, you move the variable with the negative exponent to the opposite side of the fraction to make the exponent positive.

For example:

$x^{-2} =\frac{1}{x^{2}}$

$\frac{1}{x^{-2}} =\frac{x^{2}}{1}$  or  $x^{2}$

When you have an exponent divided by an exponent, you subtract the exponents together.

For example:

$\frac{x^5}{x^2} =x^{5-2} =x^3$

$\frac{x^2}{x^1} = x^{2-1} = x^1$

When you multiply an exponent directly into a variable with an exponent, you multiply the exponents together.

For example:

$(x^{2} )^{4} = x^8$

$(\frac{x^2}{y^3} )^5=\frac{x^{10}}{y^{15}}$

$(\frac{x^1}{y^1} )^b = \frac{x^b}{y^b}$