Question

Which expressions are equivalent to this exponential expression?

Answer 1

remember that when the exponents look like this (5^2)^-3, you multiply the exponents together

when it looks like this:
5^3 x 5^2 you add the exponents
so my example would equal 5^5

also remember that you can’t have negative exponents

To solve your problem:
1. multiply the exponents here: (5^2)^-3

2. add the exponents in the next step when you multiply by the 5^4

3. now, you should get a negative exponent on the top, and you already have one on the bottom. to get rid of these negative exponents, move the one in the denominator to the numerator and vice versa

so when you move the 5^-4 in the denominator to the numerator, it becomes 5^4

4. now, you simplify. you can either subtract the exponents and do it that way, or you can solve the exponents and then divide. either way will work, although the first is easier

Answer 2

The expressions that are equivalent to the exponential expression are 5² and 25. Options B and C

To determine the equivalent expression, we need to first know that index forms are described as models used to represent numbers or variables that are too large or too small in more convenient forms.

Then, we have that the expression is given as;

(5²)⁻³ . 5⁴/5⁻⁴

expand the exponential bracket of the numerator, we have;

5⁻⁶. 5⁴/5⁻⁴

now, since the bases are the same, add the product and subtract the divisor, we have;

5⁻⁶⁺⁴⁺⁴

add the values

5²