Question

Rewrite using a single positive exponent: 4^9/4^2

Answer 1

9514 1404 393

Answer:

  4^7

Step-by-step explanation:

You know that an exponent signifies repeated multiplication. The value of the exponent is the number of times the base appears as a factor.

You also know that identical factors in the numerator and denominator of a fraction cancel.

The given fraction has 9 factors of 4 in the numerator, and 2 factors of 4 in the denominator. The two in the denominator cancel an equal number in the numerator, leaving a value that has 7 factors of 4:

  $\dfrac{4^9}{4^2}=4^{9-2}=\boxed{4^7}$