Question

Fill in the blanks with $<,>$ and $=$ sign: $7^4\_\_\_\_\_5^4$

Answer 1

Comparison of two numbers:

$$\begin{gathered} 7^4=7\times 7\times 7\times 7=2401 \\ {5}^4=5\times 5\times 5\times 5=625 \end{gathered}$$

Therefore $2401>625$

Alternatively, we know that if the exponential term with different bases but with same power then the number with the greater base is greater.

That is for $a^x$ and $b^x$ if $a>b$ then $a^x>b^x$

Since $7>5$ therefore $7^4>5^4$

Hence, the answer is $7^4>5^4$.