Question

Which expression is equivalent to 7^3⋅ 7^-5 as a fraction

Answer 1

When you multiply a base with an exponent by a base with an exponent, you add the exponents together. (But you can only combine the exponents when the bases are the same)

For example:

$x^3(x^1)=x^{(3+1)}=x^4$      (they have the same base of x)

$y^3(x^2)=y^3x^2$     (you can't combine the exponents because they have different bases of y and x)

$2^2(2^1)=2^{(2+1)}=2^3=8$

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

For example:

$x^{-3}$ or $\frac{x^{-3}}{1} =\frac{1}{x^3}$

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

$7^3*7^{-5}$      Add the exponents together

$7^{(3+(-5))}$

$7^{-2}$     Make the exponent positive

$\frac{1}{7^2}$       Simplify

$\frac{1}{49}$