find the missing value for 7^7 x 7^? = 7^11

?=

1 answer

To solve for the missing value in the equation \( 7^7 \times 7^? = 7^{11} \), we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).

Applying this property, we get:

\[ 7^7 \times 7^? = 7^{7 + ?} \]

This means:

\[ 7^{7 + ?} = 7^{11} \]

Since the bases are the same, we can set the exponents equal to each other:

\[ 7 + ? = 11 \]

To find \( ? \), subtract 7 from both sides:

\[ ? = 11 - 7 \] \[ ? = 4 \]

Thus, the missing value is \( ? = 4 \).