The repeated multiplication form shows us the meaning of a power. A power represents a product of repeated, identical factors. The exponent tells us about the number of times we need to multiply the base by itself.
an=na⋅a⋅…⋅a⋅a
We want to write the given quotient in repeated multiplication form. The expression contains two powers, so we will rewrite them both.
7679⇔7⋅7⋅7⋅7⋅7⋅77⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7
There are identical factors in the numerator and denominator of the fraction. This means that we can cross out the common factors and simplify the quotient. This is the same as dividing both numerator and denominator by the same number.
Now, we want to rewrite the expression as a power. The product contains only identical factors so we can join them all into one power.
7⋅7⋅77appears3times
The numberoftimes the 7 appears in the product is an exponent of a power. Let's finally write the power!
73
We can see that our result confirms the Quotient of Powers Property. This property states that to divide powers with the same base, we can subtract their exponents. This means that the result of 7679 is 7 raised to the power of 9−6=3, which is 73.
Mathleaks uses cookies for an enhanced user experience. By using our website, you agree to the usage of cookies as described in our policy for cookies.