Question

Which expression is equivalent to 44 ⋅ 4−9?

413
45
fraction 1 over 4 to the power 13
fraction 1 over 4 to the power 5

Answer 1

We are given expression:
`4^4`·
`4^(-9)`.

We can see that, we have both bases same.

Beses are 4 but we have different exponents.

When bases are same, we need to apply product rule of exponents.

According to this rule, we need to keep same base and add the exponents only.

`a^n * a^m = a^(m+n)`

Let us apply same rule in the given expression.

`4^4 * 4^(-9)= 4^(4+(-9))`

=
`4^(4-9) = 4^(-5)`

Now, let us apply negative exponent rule.

According to negative exponent rule, the negative exponent term goes in denomiantor by changing the negative exponent to positive exponent.

Therefore,

`4^(-5) = (1)/(4^5)`

So, the 4th option is correct.

D)
`(1)/(4^5) \ or \ ((1)/(4))^5`