Find the missing exponent.

Question

7
?
×
(
7
5
)
4
=
7
34
7
?
×(7
5
)
4
=7
34
Place only the missing exponent value in the answer box?

Answer 1

To find the missing exponent in the equation

\[ 7^? \times (7^5)^4 = 7^{34} \]

we start by simplifying the left side of the equation. Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can rewrite \((7^5)^4\) as:

\[ (7^5)^4 = 7^{5 \cdot 4} = 7^{20} \]

Now substituting this back into the equation gives us:

\[ 7^? \times 7^{20} = 7^{34} \]

Using the property of exponents \(a^m \times a^n = a^{m+n}\), we can combine the terms on the left side:

\[ 7^{? + 20} = 7^{34} \]

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

\[ ? + 20 = 34 \]

To find the missing exponent \(?\), we subtract 20 from both sides:

\[ ? = 34 - 20 = 14 \]

Thus, the missing exponent is:

\[ \boxed{14} \]