Find the numerical equivalent of 9^9⋅9^−6

Question

. Your answer should be written without exponents.

Answer 1

To simplify \( 9^9 \cdot 9^{-6} \), we can use the property of exponents which states that when multiplying two exponents with the same base, we add the exponents:

\[ 9^9 \cdot 9^{-6} = 9^{9 + (-6)} = 9^{9 - 6} = 9^3 \]

Next, we need to calculate \( 9^3 \):

\[ 9^3 = 9 \cdot 9 \cdot 9 \]

Calculating \( 9 \cdot 9 \):

\[ 9 \cdot 9 = 81 \]

Then multiplying by 9 again:

\[ 81 \cdot 9 = 729 \]

Thus, the numerical equivalent of \( 9^9 \cdot 9^{-6} \) is

\[ \boxed{729} \]

Answer 2

WITHOUT exponents

Answer 3

Apologies for misunderstanding your request. Let's calculate \( 9^9 \cdot 9^{-6} \) without using exponents.

First, we know from the previous steps:

\[ 9^9 \cdot 9^{-6} = 9^3 \]

Now, we'll compute \( 9^3 \) step by step without using exponents:

1. \( 9 \times 9 = 81 \)
2. Then, \( 81 \times 9 \):

\[ 81 \times 9 = 729 \]

So, without using exponents, the numerical equivalent of \( 9^9 \cdot 9^{-6} \) is

\[ \boxed{729} \]