Find the numerical equivalent of 9 to the power of 9⋅ 9 to the power of −6

Question

. Your answer should be written without exponents.
the answer is 7 to the power of 29
true or false

Answer 1

To solve the expression \( 9^9 \cdot 9^{-6} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Applying this property:

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

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

\[ 9^3 = 729 \]

Now we need to determine whether \( 729 \) is equivalent to \( 7^{29} \).

Since \( 7^{29} \) is an extremely large number, we can conclude that:

\[ 729 \neq 7^{29} \]

Thus, the statement "the answer is \( 7^{29} \)" is false.