Question

what is an equivalent expression to (15^-3*4^7)^0/4^3 that has been generated by applying the properties of intergers exponents

Answer 1

To find an equivalent expression by applying the properties of integer exponents, we can simplify each part separately:

First, let's simplify the expression inside the parentheses: (15^-3 * 4^7)

15^-3 means "1 divided by 15 to the power of 3," which can be rewritten as 1/15^3.

So, the expression becomes [(1/15^3) * 4^7].

Next, we simplify the expression 1/15^3.

15^3 means "15 raised to the power of 3," which is equal to 15 * 15 * 15 = 3375.

Therefore, 1/15^3 can be rewritten as 1/3375.

Now, the expression becomes [(1/3375) * 4^7].

Next, let's simplify the expression outside the parentheses: [(1/3375) * 4^7]^0/4^3.

(4^7)^0 means any number raised to the power of 0 is 1.

So, the expression becomes (1/3375)^0/4^3.

Lastly, let's simplify the expression 1/3375.

1/3375 cannot be simplified further.

Therefore, the final equivalent expression is 1^0/4^3, which simplifies to 1/4^3.

Thus, the equivalent expression is 1/64.